diff --git a/Library/Homebrew/bundle.rb b/Library/Homebrew/bundle.rb
index 8c13ae9e52287..3052bf4dadda7 100644
--- a/Library/Homebrew/bundle.rb
+++ b/Library/Homebrew/bundle.rb
@@ -101,7 +101,7 @@ def which_formula?(name)
         which(name).present?
       end
 
-      sig { params(block: T.proc.returns(T.anything)).returns(T.untyped) }
+      sig { type_parameters(:U).params(block: T.proc.returns(T.type_parameter(:U))).returns(T.type_parameter(:U)) }
       def exchange_uid_if_needed!(&block)
         euid = Process.euid
         uid = Process.uid
diff --git a/Library/Homebrew/cache_store.rb b/Library/Homebrew/cache_store.rb
index d9c2440f7043b..d71766b984281 100644
--- a/Library/Homebrew/cache_store.rb
+++ b/Library/Homebrew/cache_store.rb
@@ -22,9 +22,9 @@ class CacheStoreDatabase
       .returns(T.type_parameter(:U))
   }
   def self.use(type, &_blk)
-    @db_type_reference_hash ||= T.let({}, T.nilable(T::Hash[T.untyped, T.untyped]))
-    @db_type_reference_hash[type] ||= {}
-    type_ref = @db_type_reference_hash[type]
+    @db_type_reference_hash ||= T.let({}, T.nilable(T::Hash[Symbol, { count: Integer, db: CacheStoreDatabase }]))
+    @db_type_reference_hash[type] ||= { count: 0, db: CacheStoreDatabase.new(type) }
+    type_ref = @db_type_reference_hash.fetch(type)
 
     type_ref[:count] ||= 0
     type_ref[:count]  += 1
diff --git a/Library/Homebrew/cask/artifact/app.rb b/Library/Homebrew/cask/artifact/app.rb
index d1a86d59d0c00..dbae46760ccfb 100644
--- a/Library/Homebrew/cask/artifact/app.rb
+++ b/Library/Homebrew/cask/artifact/app.rb
@@ -8,7 +8,7 @@ module Artifact
     # Artifact corresponding to the `app` stanza.
     class App < Moved
       sig {
-        params(
+        override.params(
           adopt:        T::Boolean,
           auto_updates: T.nilable(T::Boolean),
           force:        T::Boolean,
diff --git a/Library/Homebrew/cask/artifact/artifact.rb b/Library/Homebrew/cask/artifact/artifact.rb
index 7d39512db8c2c..9cd30a479b3a9 100644
--- a/Library/Homebrew/cask/artifact/artifact.rb
+++ b/Library/Homebrew/cask/artifact/artifact.rb
@@ -12,20 +12,21 @@ def self.english_name
         "Generic Artifact"
       end
 
-      sig { params(cask: Cask, args: T.untyped).returns(T.attached_class) }
-      def self.from_args(cask, *args)
-        source, options = args
-
+      sig { params(cask: Cask, source: T.nilable(String), target_hash: T.anything).returns(Relocated) }
+      def self.from_args(cask, source = nil, **target_hash)
         raise CaskInvalidError.new(cask.token, "No source provided for #{english_name}.") if source.blank?
 
-        unless options&.key?(:target)
+        unless target_hash.key?(:target)
           raise CaskInvalidError.new(cask.token, "#{english_name} '#{source}' requires a target.")
         end
 
-        new(cask, source, **options)
+        new(cask, source, **target_hash)
       end
 
-      sig { params(target: T.any(String, Pathname)).returns(Pathname) }
+      # FIXME: This is a pre-existing violation
+      # rubocop:disable Sorbet/AllowIncompatibleOverride
+      sig { override(allow_incompatible: true).params(target: T.any(String, Pathname)).returns(Pathname) }
+      # rubocop:enable Sorbet/AllowIncompatibleOverride
       def resolve_target(target)
         super(target, base_dir: nil)
       end
diff --git a/Library/Homebrew/cask/artifact/bashcompletion.rb b/Library/Homebrew/cask/artifact/bashcompletion.rb
index 3ffe7c6833f9d..5b5d34825ffc1 100644
--- a/Library/Homebrew/cask/artifact/bashcompletion.rb
+++ b/Library/Homebrew/cask/artifact/bashcompletion.rb
@@ -7,7 +7,10 @@ module Cask
   module Artifact
     # Artifact corresponding to the `bash_completion` stanza.
     class BashCompletion < ShellCompletion
-      sig { params(target: T.any(String, Pathname)).returns(Pathname) }
+      # FIXME: This is a pre-existing violation
+      # rubocop:disable Sorbet/AllowIncompatibleOverride
+      sig { override(allow_incompatible: true).params(target: T.any(String, Pathname)).returns(Pathname) }
+      # rubocop:enable Sorbet/AllowIncompatibleOverride
       def resolve_target(target)
         name = if File.extname(target).nil?
           target
diff --git a/Library/Homebrew/cask/artifact/binary.rb b/Library/Homebrew/cask/artifact/binary.rb
index 56b47a6826cfd..fbe5a994c4626 100644
--- a/Library/Homebrew/cask/artifact/binary.rb
+++ b/Library/Homebrew/cask/artifact/binary.rb
@@ -1,4 +1,4 @@
-# typed: true # rubocop:todo Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 require "cask/artifact/symlinked"
@@ -7,7 +7,8 @@ module Cask
   module Artifact
     # Artifact corresponding to the `binary` stanza.
     class Binary < Symlinked
-      def link(command: nil, **options)
+      sig { override.params(command: T.class_of(SystemCommand), force: T::Boolean, adopt: T::Boolean, _options: T.anything).void }
+      def link(command:, force: false, adopt: false, **_options)
         super
         return if source.executable?
 
diff --git a/Library/Homebrew/cask/artifact/fishcompletion.rb b/Library/Homebrew/cask/artifact/fishcompletion.rb
index ef4e13c8cdbbf..8ac2834cf82da 100644
--- a/Library/Homebrew/cask/artifact/fishcompletion.rb
+++ b/Library/Homebrew/cask/artifact/fishcompletion.rb
@@ -7,7 +7,10 @@ module Cask
   module Artifact
     # Artifact corresponding to the `fish_completion` stanza.
     class FishCompletion < ShellCompletion
-      sig { params(target: T.any(String, Pathname)).returns(Pathname) }
+      # FIXME: This is a pre-existing violation
+      # rubocop:disable Sorbet/AllowIncompatibleOverride
+      sig { override(allow_incompatible: true).params(target: T.any(String, Pathname)).returns(Pathname) }
+      # rubocop:enable Sorbet/AllowIncompatibleOverride
       def resolve_target(target)
         name = if target.to_s.end_with? ".fish"
           target
diff --git a/Library/Homebrew/cask/artifact/installer.rb b/Library/Homebrew/cask/artifact/installer.rb
index 43e042e5d1889..844fac2387e1b 100644
--- a/Library/Homebrew/cask/artifact/installer.rb
+++ b/Library/Homebrew/cask/artifact/installer.rb
@@ -1,4 +1,4 @@
-# typed: true # rubocop:todo Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 require "cask/artifact/abstract_artifact"
@@ -8,12 +8,13 @@ module Cask
   module Artifact
     # Artifact corresponding to the `installer` stanza.
     class Installer < AbstractArtifact
-      VALID_KEYS = Set.new([
-        :manual,
-        :script,
-      ]).freeze
+      VALID_KEYS = T.let(
+        Set.new([:manual, :script]).freeze,
+        T::Set[Symbol],
+      )
 
-      def install_phase(command: nil, **_)
+      sig { params(command: T.class_of(SystemCommand), _options: T.anything).void }
+      def install_phase(command:, **_options)
         if manual_install
           puts <<~EOS
             Cask #{cask} only provides a manual installer. To run it and complete the installation:
@@ -35,6 +36,7 @@ def install_phase(command: nil, **_)
         end
       end
 
+      sig { params(cask: Cask, args: DirectivesType).returns(Installer) }
       def self.from_args(cask, **args)
         raise CaskInvalidError.new(cask, "'installer' stanza requires an argument.") if args.empty?
 
@@ -59,18 +61,23 @@ def self.from_args(cask, **args)
         new(cask, **args)
       end
 
-      attr_reader :path, :args
+      sig { returns(Pathname) }
+      attr_reader :path
+
+      sig { returns(T::Hash[Symbol, DirectivesType]) }
+      attr_reader :args
 
       sig { returns(T::Boolean) }
       attr_reader :manual_install
 
+      sig { params(cask: Cask, args: DirectivesType).void }
       def initialize(cask, **args)
         super
 
-        if args.key?(:manual)
-          @path = Pathname(args[:manual])
-          @args = []
-          @manual_install = true
+        if (manual = T.cast(args[:manual], T.nilable(String)))
+          @path = T.let(Pathname(manual), Pathname)
+          @args = T.let({}, T::Hash[Symbol, DirectivesType])
+          @manual_install = T.let(true, T::Boolean)
         else
           path, @args = self.class.read_script_arguments(
             args[:script], self.class.dsl_key.to_s, { must_succeed: true, sudo: false }, print_stdout: true
@@ -85,10 +92,9 @@ def initialize(cask, **args)
       sig { override.returns(String) }
       def summarize = path.to_s
 
+      sig { returns(T::Hash[Symbol, T.anything]) }
       def to_h
-        { path: }.tap do |h|
-          h[:args] = args unless manual_install
-        end
+        manual_install ? { path: } : { path:, args: }
       end
     end
   end
diff --git a/Library/Homebrew/cask/artifact/keyboard_layout.rb b/Library/Homebrew/cask/artifact/keyboard_layout.rb
index b1e72ccaaff5c..f2a3f6b7bea9a 100644
--- a/Library/Homebrew/cask/artifact/keyboard_layout.rb
+++ b/Library/Homebrew/cask/artifact/keyboard_layout.rb
@@ -1,4 +1,4 @@
-# typed: true # rubocop:todo Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 require "cask/artifact/moved"
@@ -7,19 +7,22 @@ module Cask
   module Artifact
     # Artifact corresponding to the `keyboard_layout` stanza.
     class KeyboardLayout < Moved
-      def install_phase(**options)
+      sig { override.params(command: T.class_of(SystemCommand), options: T.anything).void }
+      def install_phase(command:, **options)
         super
         delete_keyboard_layout_cache(**options)
       end
 
-      def uninstall_phase(**options)
+      sig { override.params(command: T.class_of(SystemCommand), options: T.anything).void }
+      def uninstall_phase(command:, **options)
         super
         delete_keyboard_layout_cache(**options)
       end
 
       private
 
-      def delete_keyboard_layout_cache(command: nil, **_)
+      sig { params(command: T.class_of(SystemCommand), _options: T.anything).void }
+      def delete_keyboard_layout_cache(command:, **_options)
         command.run!(
           "/bin/rm",
           args:         ["-f", "--", "/System/Library/Caches/com.apple.IntlDataCache.le*"],
diff --git a/Library/Homebrew/cask/artifact/manpage.rb b/Library/Homebrew/cask/artifact/manpage.rb
index 170a0904d3b5b..514fe326531f7 100644
--- a/Library/Homebrew/cask/artifact/manpage.rb
+++ b/Library/Homebrew/cask/artifact/manpage.rb
@@ -1,4 +1,4 @@
-# typed: true # rubocop:todo Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 require "cask/artifact/symlinked"
@@ -7,9 +7,11 @@ module Cask
   module Artifact
     # Artifact corresponding to the `manpage` stanza.
     class Manpage < Symlinked
+      sig { returns(String) }
       attr_reader :section
 
-      def self.from_args(cask, source)
+      sig { params(cask: Cask, source: String, _target_hash: T.anything).returns(Manpage) }
+      def self.from_args(cask, source, **_target_hash)
         section = source.to_s[/\.([1-8]|n|l)(?:\.gz)?$/, 1]
 
         raise CaskInvalidError, "'#{source}' is not a valid man page name" unless section
@@ -17,12 +19,17 @@ def self.from_args(cask, source)
         new(cask, source, section)
       end
 
+      sig { params(cask: Cask, source: String, section: String).void }
       def initialize(cask, source, section)
         @section = section
 
         super(cask, source)
       end
 
+      # FIXME: This is a pre-existing violation
+      # rubocop:disable Sorbet/AllowIncompatibleOverride
+      sig { override(allow_incompatible: true).params(target: T.any(String, Pathname)).returns(Pathname) }
+      # rubocop:enable Sorbet/AllowIncompatibleOverride
       def resolve_target(target)
         config.manpagedir.join("man#{section}", target)
       end
diff --git a/Library/Homebrew/cask/artifact/mdimporter.rb b/Library/Homebrew/cask/artifact/mdimporter.rb
index da83a909e4779..42747daa80641 100644
--- a/Library/Homebrew/cask/artifact/mdimporter.rb
+++ b/Library/Homebrew/cask/artifact/mdimporter.rb
@@ -1,4 +1,4 @@
-# typed: true # rubocop:todo Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 require "cask/artifact/moved"
@@ -12,14 +12,36 @@ def self.english_name
         "Spotlight metadata importer"
       end
 
-      def install_phase(**options)
+      sig {
+        override.params(
+          adopt:        T::Boolean,
+          auto_updates: T.nilable(T::Boolean),
+          force:        T::Boolean,
+          verbose:      T::Boolean,
+          predecessor:  T.nilable(Cask),
+          successor:    T.nilable(Cask),
+          reinstall:    T::Boolean,
+          command:      T.class_of(SystemCommand),
+        ).void
+      }
+      def install_phase(
+        adopt: false,
+        auto_updates: false,
+        force: false,
+        verbose: false,
+        predecessor: nil,
+        successor: nil,
+        reinstall: false,
+        command: SystemCommand
+      )
         super
-        reload_spotlight(**options)
+        reload_spotlight(command:)
       end
 
       private
 
-      def reload_spotlight(command: nil, **_)
+      sig { params(command: T.class_of(SystemCommand)).void }
+      def reload_spotlight(command:)
         command.run!("/usr/bin/mdimport", args: ["-r", target])
       end
     end
diff --git a/Library/Homebrew/cask/artifact/moved.rb b/Library/Homebrew/cask/artifact/moved.rb
index ba0c2a8ee3a1d..1d24ec8f239be 100644
--- a/Library/Homebrew/cask/artifact/moved.rb
+++ b/Library/Homebrew/cask/artifact/moved.rb
@@ -1,4 +1,4 @@
-# typed: true # rubocop:todo Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 require "cask/artifact/relocated"
@@ -13,14 +13,37 @@ def self.english_description
         "#{english_name}s"
       end
 
-      def install_phase(**options)
-        move(**options)
+      sig {
+        overridable.params(
+          adopt:        T::Boolean,
+          auto_updates: T.nilable(T::Boolean),
+          force:        T::Boolean,
+          verbose:      T::Boolean,
+          predecessor:  T.nilable(Cask),
+          successor:    T.nilable(Cask),
+          reinstall:    T::Boolean,
+          command:      T.class_of(SystemCommand),
+        ).void
+      }
+      def install_phase(
+        adopt: false,
+        auto_updates: false,
+        force: false,
+        verbose: false,
+        predecessor: nil,
+        successor: nil,
+        reinstall: false,
+        command: SystemCommand
+      )
+        move(adopt:, auto_updates:, force:, verbose:, predecessor:, successor:, reinstall:, command:)
       end
 
-      def uninstall_phase(**options)
-        move_back(**options)
+      sig { overridable.params(command: T.class_of(SystemCommand), options: T.anything).void }
+      def uninstall_phase(command:, **options)
+        move_back(command:, **options)
       end
 
+      sig { overridable.returns(String) }
       def summarize_installed
         if target.exist?
           "#{printable_target} (#{target.abv})"
@@ -31,8 +54,13 @@ def summarize_installed
 
       private
 
-      def move(adopt: false, auto_updates: false, force: false, verbose: false, predecessor: nil, reinstall: false,
-               command: nil, **options)
+      sig {
+        params(command: T.class_of(SystemCommand), adopt: T::Boolean, auto_updates: T.nilable(T::Boolean),
+               force: T::Boolean, verbose: T::Boolean, predecessor: T.nilable(Cask), reinstall: T::Boolean,
+               options: T.anything).void
+      }
+      def move(command:, adopt: false, auto_updates: false, force: false, verbose: false, predecessor: nil,
+               reinstall: false, **options)
         unless source.exist?
           raise CaskError, "It seems the #{self.class.english_name} source '#{source}' is not there."
         end
@@ -128,12 +156,14 @@ def move(adopt: false, auto_updates: false, force: false, verbose: false, predec
       end
 
       # Performs any actions necessary after the source has been moved to the target location.
+      sig { params(command: T.class_of(SystemCommand)).void }
       def post_move(command)
         FileUtils.ln_sf target, source
 
         add_altname_metadata(target, source.basename, command:)
       end
 
+      sig { params(cask: T.nilable(Cask)).returns(T::Boolean) }
       def matching_artifact?(cask)
         return false unless cask
 
@@ -142,7 +172,8 @@ def matching_artifact?(cask)
         end
       end
 
-      def move_back(skip: false, force: false, adopt: false, command: nil, **options)
+      sig { params(command: T.class_of(SystemCommand), skip: T::Boolean, force: T::Boolean, adopt: T::Boolean, options: T.anything).void }
+      def move_back(command:, skip: false, force: false, adopt: false, **options)
         FileUtils.rm source if source.symlink? && source.dirname.join(source.readlink) == target
 
         if Utils.path_occupied?(source)
@@ -178,7 +209,8 @@ def move_back(skip: false, force: false, adopt: false, command: nil, **options)
         delete(target, force:, command:, **options)
       end
 
-      def delete(target, force: false, successor: nil, command: nil, **_)
+      sig { params(target: Pathname, command: T.class_of(SystemCommand), force: T::Boolean, successor: T.nilable(Cask), _options: T.anything).void }
+      def delete(target, command:, force: false, successor: nil, **_options)
         ohai "Removing #{self.class.english_name} '#{target}'"
         raise CaskError, "Cannot remove undeletable #{self.class.english_name}." if undeletable?(target)
 
diff --git a/Library/Homebrew/cask/artifact/pkg.rb b/Library/Homebrew/cask/artifact/pkg.rb
index d3bef370e81ae..7edbf6fe9fee7 100644
--- a/Library/Homebrew/cask/artifact/pkg.rb
+++ b/Library/Homebrew/cask/artifact/pkg.rb
@@ -1,4 +1,4 @@
-# typed: true # rubocop:todo Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 require "plist"
@@ -11,30 +11,48 @@ module Cask
   module Artifact
     # Artifact corresponding to the `pkg` stanza.
     class Pkg < AbstractArtifact
-      attr_reader :path, :stanza_options
+      Choices = T.type_alias { T.nilable(T.any(T::Array[T::Hash[T.anything, T.anything]], T::Hash[Symbol, T.anything])) }
+      private_constant :Choices
+      StanzaOptions = T.type_alias { { allow_untrusted: T.nilable(T::Boolean), choices: Choices } }
+      private_constant :StanzaOptions
 
+      sig { returns(Pathname) }
+      attr_reader :path
+
+      sig { returns(T::Hash[Symbol, T.anything]) }
+      attr_reader :stanza_options
+
+      # sig { params(cask: Cask, path: String, allow_untrusted: T.nilable(T::Boolean), choices: Choices).returns(Pkg) }
+      # def self.from_args(cask, path, allow_untrusted: nil, choices: nil)
+      sig { params(cask: Cask, path: String, stanza_options: T.anything).returns(Pkg) }
       def self.from_args(cask, path, **stanza_options)
         stanza_options.assert_valid_keys(:allow_untrusted, :choices)
         new(cask, path, **stanza_options)
       end
 
+      # sig { params(cask: Cask, path: String, allow_untrusted: T.nilable(T::Boolean), choices: Choices).void }
+      # def initialize(cask, path, allow_untrusted: nil, choices: nil)
+      sig { params(cask: Cask, path: String, stanza_options: T.anything).void }
       def initialize(cask, path, **stanza_options)
         super
-        @path = cask.staged_path.join(path)
-        @stanza_options = stanza_options
+        @path = T.let(cask.staged_path.join(path), Pathname)
+        @stanza_options = T.let(stanza_options, T::Hash[Symbol, T.anything])
       end
 
+      sig { override.returns(String) }
       def summarize
         path.relative_path_from(cask.staged_path).to_s
       end
 
-      def install_phase(**options)
-        run_installer(**options)
+      sig { params(command: T.class_of(SystemCommand), options: T.anything).void }
+      def install_phase(command:, **options)
+        run_installer(command:, **options)
       end
 
       private
 
-      def run_installer(command: nil, verbose: false, **_options)
+      sig { params(command: T.class_of(SystemCommand), verbose: T::Boolean, _options: T.anything).void }
+      def run_installer(command:, verbose: false, **_options)
         ohai "Running installer for #{cask} with `sudo` (which may request your password)..."
         unless path.exist?
           pkg = path.relative_path_from(cask.staged_path)
@@ -71,9 +89,10 @@ def run_installer(command: nil, verbose: false, **_options)
         end
       end
 
-      def with_choices_file
+      sig { params(_block: T.proc.params(file_path: T.nilable(String)).void).void }
+      def with_choices_file(&_block)
         choices = stanza_options.fetch(:choices, {})
-        return yield nil if choices.empty?
+        return yield nil if T.unsafe(choices).empty?
 
         Tempfile.open(["choices", ".xml"]) do |file|
           file.write Plist::Emit.dump(choices)
diff --git a/Library/Homebrew/cask/artifact/qlplugin.rb b/Library/Homebrew/cask/artifact/qlplugin.rb
index 4e0c2430f8079..86bf097c7cdad 100644
--- a/Library/Homebrew/cask/artifact/qlplugin.rb
+++ b/Library/Homebrew/cask/artifact/qlplugin.rb
@@ -1,4 +1,4 @@
-# typed: true # rubocop:todo Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 require "cask/artifact/moved"
@@ -12,19 +12,22 @@ def self.english_name
         "Quick Look Plugin"
       end
 
-      def install_phase(**options)
+      sig { override.params(command: T.class_of(SystemCommand), options: T.anything).void }
+      def install_phase(command:, **options)
         super
-        reload_quicklook(**options)
+        reload_quicklook(command:, **options)
       end
 
-      def uninstall_phase(**options)
+      sig { override.params(command: T.class_of(SystemCommand), options: T.anything).void }
+      def uninstall_phase(command:, **options)
         super
-        reload_quicklook(**options)
+        reload_quicklook(command:, **options)
       end
 
       private
 
-      def reload_quicklook(command: nil, **_)
+      sig { params(command: T.class_of(SystemCommand), _options: T.anything).void }
+      def reload_quicklook(command:, **_options)
         command.run!("/usr/bin/qlmanage", args: ["-r"])
       end
     end
diff --git a/Library/Homebrew/cask/artifact/relocated.rb b/Library/Homebrew/cask/artifact/relocated.rb
index 24373ccf749eb..cbee4a9ee076b 100644
--- a/Library/Homebrew/cask/artifact/relocated.rb
+++ b/Library/Homebrew/cask/artifact/relocated.rb
@@ -1,4 +1,4 @@
-# typed: true # rubocop:todo Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 require "cask/artifact/abstract_artifact"
@@ -8,20 +8,16 @@ module Cask
   module Artifact
     # Superclass for all artifacts which have a source and a target location.
     class Relocated < AbstractArtifact
-      def self.from_args(cask, *args)
-        source_string, target_hash = args
-
-        if target_hash
-          raise CaskInvalidError, cask unless target_hash.respond_to?(:keys)
-
-          target_hash.assert_valid_keys(:target)
-        end
-
-        target_hash ||= {}
+      sig {
+        params(cask: Cask, source_string: T.nilable(String), target_hash: DirectivesType).returns(Relocated)
+      }
+      def self.from_args(cask, source_string = nil, **target_hash)
+        target_hash.assert_valid_keys(:target)
 
         new(cask, source_string, **target_hash)
       end
 
+      sig { overridable.params(target: T.any(String, Pathname), base_dir: T.nilable(Pathname)).returns(Pathname) }
       def resolve_target(target, base_dir: config.public_send(self.class.dirmethod))
         target = Pathname(target)
 
@@ -33,20 +29,18 @@ def resolve_target(target, base_dir: config.public_send(self.class.dirmethod))
         target
       end
 
-      sig {
-        params(cask: Cask, source: T.nilable(T.any(String, Pathname)), target_hash: T.any(String, Pathname))
-          .void
-      }
+      sig { params(cask: Cask, source: T.nilable(T.any(String, Pathname)), target_hash: DirectivesType).void }
       def initialize(cask, source, **target_hash)
         super
 
         target = target_hash[:target]
-        @source = nil
-        @source_string = source.to_s
-        @target = nil
-        @target_string = target.to_s
+        @source = T.let(nil, T.nilable(Pathname))
+        @source_string = T.let(source.to_s, String)
+        @target = T.let(nil, T.nilable(Pathname))
+        @target_string = T.let(target.to_s, String)
       end
 
+      sig { returns(Pathname) }
       def source
         @source ||= begin
           base_path = cask.staged_path
@@ -55,10 +49,12 @@ def source
         end
       end
 
+      sig { returns(Pathname) }
       def target
         @target ||= resolve_target(@target_string.presence || source.basename)
       end
 
+      sig { returns(T::Array[T.anything]) }
       def to_a
         [@source_string].tap do |ary|
           ary << { target: @target_string } unless @target_string.empty?
@@ -103,6 +99,7 @@ def add_altname_metadata(file, altname, command:)
                      sudo:         !file.writable?)
       end
 
+      sig { returns(String) }
       def printable_target
         target.to_s.sub(/^#{Dir.home}(#{File::SEPARATOR}|$)/, "~/")
       end
diff --git a/Library/Homebrew/cask/artifact/shellcompletion.rb b/Library/Homebrew/cask/artifact/shellcompletion.rb
index 54bac0ec7ddcc..f908f82e97925 100644
--- a/Library/Homebrew/cask/artifact/shellcompletion.rb
+++ b/Library/Homebrew/cask/artifact/shellcompletion.rb
@@ -6,8 +6,13 @@
 module Cask
   module Artifact
     class ShellCompletion < Symlinked
-      sig { params(_: T.any(String, Pathname)).returns(Pathname) }
-      def resolve_target(_)
+      sig {
+        override
+          .overridable
+          .params(_target: T.any(String, Pathname), base_dir: T.nilable(Pathname))
+          .returns(T.noreturn)
+      }
+      def resolve_target(_target, base_dir: nil)
         raise CaskInvalidError, "Shell completion without shell info"
       end
     end
diff --git a/Library/Homebrew/cask/artifact/stage_only.rb b/Library/Homebrew/cask/artifact/stage_only.rb
index 5a1cb6f9d0e70..9362abc6f67a0 100644
--- a/Library/Homebrew/cask/artifact/stage_only.rb
+++ b/Library/Homebrew/cask/artifact/stage_only.rb
@@ -1,4 +1,4 @@
-# typed: true # rubocop:todo Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 require "cask/artifact/abstract_artifact"
@@ -7,8 +7,9 @@ module Cask
   module Artifact
     # Artifact corresponding to the `stage_only` stanza.
     class StageOnly < AbstractArtifact
-      def self.from_args(cask, *args, **kwargs)
-        if (args != [true] && args != ["true"]) || kwargs.present?
+      sig { params(cask: Cask, arg: T.any(String, TrueClass)).returns(StageOnly) }
+      def self.from_args(cask, arg)
+        unless [true, "true"].include?(arg)
           raise CaskInvalidError.new(cask.token, "'stage_only' takes only a single argument: true")
         end
 
diff --git a/Library/Homebrew/cask/artifact/symlinked.rb b/Library/Homebrew/cask/artifact/symlinked.rb
index ba03e8d99d1d2..01f370a3321c7 100644
--- a/Library/Homebrew/cask/artifact/symlinked.rb
+++ b/Library/Homebrew/cask/artifact/symlinked.rb
@@ -1,4 +1,4 @@
-# typed: true # rubocop:todo Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 require "cask/artifact/relocated"
@@ -17,14 +17,17 @@ def self.english_description
         "#{english_name} #{link_type_english_name}s"
       end
 
+      sig { params(options: T.anything).void }
       def install_phase(**options)
         link(**options)
       end
 
+      sig { params(options: T.anything).void }
       def uninstall_phase(**options)
         unlink(**options)
       end
 
+      sig { returns(String) }
       def summarize_installed
         if target.symlink? && target.exist? && target.readlink.exist?
           "#{printable_target} -> #{target.readlink} (#{target.readlink.abv})"
@@ -41,7 +44,8 @@ def summarize_installed
 
       private
 
-      def link(force: false, adopt: false, command: nil, **_options)
+      sig { overridable.params(command: T.class_of(SystemCommand), force: T::Boolean, adopt: T::Boolean, _options: T.anything).void }
+      def link(command:, force: false, adopt: false, **_options)
         unless source.exist?
           raise CaskError,
                 "It seems the #{self.class.link_type_english_name.downcase} " \
@@ -68,7 +72,8 @@ def link(force: false, adopt: false, command: nil, **_options)
         create_filesystem_link(command)
       end
 
-      def unlink(command: nil, **)
+      sig { params(command: T.class_of(SystemCommand), _options: T.anything).void }
+      def unlink(command:, **_options)
         return unless target.symlink?
 
         ohai "Unlinking #{self.class.english_name} '#{target}'"
diff --git a/Library/Homebrew/cask/artifact/uninstall.rb b/Library/Homebrew/cask/artifact/uninstall.rb
index 8dbcf1afc8e18..dbd2fd6d77e66 100644
--- a/Library/Homebrew/cask/artifact/uninstall.rb
+++ b/Library/Homebrew/cask/artifact/uninstall.rb
@@ -1,4 +1,4 @@
-# typed: true # rubocop:todo Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 require "cask/artifact/abstract_uninstall"
@@ -9,10 +9,8 @@ module Artifact
     class Uninstall < AbstractUninstall
       UPGRADE_REINSTALL_SKIP_DIRECTIVES = [:quit, :signal].freeze
 
-      def uninstall_phase(**options)
-        upgrade   = options.fetch(:upgrade, false)
-        reinstall = options.fetch(:reinstall, false)
-
+      sig { params(upgrade: T::Boolean, reinstall: T::Boolean, options: T.anything).void }
+      def uninstall_phase(upgrade: false, reinstall: false, **options)
         raw_on_upgrade = directives[:on_upgrade]
         on_upgrade_syms =
           case raw_on_upgrade
@@ -42,6 +40,7 @@ def uninstall_phase(**options)
         end
       end
 
+      sig { params(options: T.anything).void }
       def post_uninstall_phase(**options)
         dispatch_uninstall_directive(:rmdir, **options)
       end
diff --git a/Library/Homebrew/cask/artifact/zshcompletion.rb b/Library/Homebrew/cask/artifact/zshcompletion.rb
index 971de918570c9..233883f605bcf 100644
--- a/Library/Homebrew/cask/artifact/zshcompletion.rb
+++ b/Library/Homebrew/cask/artifact/zshcompletion.rb
@@ -7,7 +7,10 @@ module Cask
   module Artifact
     # Artifact corresponding to the `zsh_completion` stanza.
     class ZshCompletion < ShellCompletion
-      sig { params(target: T.any(String, Pathname)).returns(Pathname) }
+      # FIXME: This is a pre-existing violation
+      # rubocop:disable Sorbet/AllowIncompatibleOverride
+      sig { override(allow_incompatible: true).params(target: T.any(String, Pathname)).returns(Pathname) }
+      # rubocop:enable Sorbet/AllowIncompatibleOverride
       def resolve_target(target)
         name = if target.to_s.start_with? "_"
           target
diff --git a/Library/Homebrew/cask/artifact_set.rb b/Library/Homebrew/cask/artifact_set.rb
index 8f1da460b4594..7c68538275b28 100644
--- a/Library/Homebrew/cask/artifact_set.rb
+++ b/Library/Homebrew/cask/artifact_set.rb
@@ -8,7 +8,7 @@ class ArtifactSet < ::Set
 
     Elem = type_member(:out) { { fixed: Artifact::AbstractArtifact } }
 
-    sig { params(block: T.nilable(T.proc.params(arg0: Elem).returns(T.untyped))).void }
+    sig { override.params(block: T.nilable(T.proc.params(arg0: Elem).returns(BasicObject))).returns(T.untyped) }
     def each(&block)
       return enum_for(T.must(__method__)) { size } unless block
 
diff --git a/Library/Homebrew/cask/pkg.rb b/Library/Homebrew/cask/pkg.rb
index 2f1241fda90a0..fb74e4a70dd63 100644
--- a/Library/Homebrew/cask/pkg.rb
+++ b/Library/Homebrew/cask/pkg.rb
@@ -104,9 +104,12 @@ def root
       @root ||= T.let(Pathname.new(info.fetch("volume")).join(info.fetch("install-location")), T.nilable(Pathname))
     end
 
-    sig { returns(T.untyped) }
+    sig { returns(T::Hash[String, T.untyped]) }
     def info
-      @info ||= T.let(@command.run!("/usr/sbin/pkgutil", args: ["--pkg-info-plist", package_id]).plist, T.untyped)
+      @info ||= T.let(
+        @command.run!("/usr/sbin/pkgutil", args: ["--pkg-info-plist", package_id]).plist,
+        T.nilable(T::Hash[String, T.untyped]),
+      )
     end
 
     private
diff --git a/Library/Homebrew/dev-cmd/extract.rb b/Library/Homebrew/dev-cmd/extract.rb
index f9f1d8b79adeb..73bd81b9b2ace 100644
--- a/Library/Homebrew/dev-cmd/extract.rb
+++ b/Library/Homebrew/dev-cmd/extract.rb
@@ -172,7 +172,7 @@ def formula_at_revision(repo, name, file, rev)
         with_monkey_patch { Formulary.from_contents(name, file, contents, ignore_errors: true) }
       end
 
-      sig { params(_block: T.proc.void).returns(T.untyped) }
+      sig { type_parameters(:U).params(_block: T.proc.returns(T.type_parameter(:U))).returns(T.type_parameter(:U)) }
       def with_monkey_patch(&_block)
         # Since `method_defined?` is not a supported type guard, the use of `alias_method` below is not typesafe:
         BottleSpecification.class_eval do