diff --git a/Library/Homebrew/cask/cask_loader.rb b/Library/Homebrew/cask/cask_loader.rb
index 5223ad2ee8..c62af1c1e3 100644
--- a/Library/Homebrew/cask/cask_loader.rb
+++ b/Library/Homebrew/cask/cask_loader.rb
@@ -167,7 +167,9 @@ module Cask
 
       def initialize(tapped_name)
         user, repo, token = tapped_name.split("/", 3)
-        super Tap.fetch(user, repo).cask_dir/"#{token}.rb"
+        tap = Tap.fetch(user, repo)
+        cask = CaskLoader.find_cask_in_tap(token, tap)
+        super cask
       end
 
       def load(config:)
@@ -421,8 +423,15 @@ module Cask
     end
 
     def self.tap_paths(token)
-      Tap.map { |t| t.cask_dir/"#{token.to_s.downcase}.rb" }
-         .select(&:exist?)
+      Tap.map do |tap|
+        find_cask_in_tap(token.to_s.downcase, tap)
+      end.select(&:exist?)
+    end
+
+    def self.find_cask_in_tap(token, tap)
+      filename = "#{token}.rb"
+
+      Tap.cask_files_by_name(tap).fetch(filename, tap.cask_dir/filename)
     end
   end
 end
diff --git a/Library/Homebrew/cmd/tap-info.rb b/Library/Homebrew/cmd/tap-info.rb
index d97b6168d0..f72c611abd 100644
--- a/Library/Homebrew/cmd/tap-info.rb
+++ b/Library/Homebrew/cmd/tap-info.rb
@@ -50,17 +50,14 @@ module Homebrew
       tap_count = 0
       formula_count = 0
       command_count = 0
-      pinned_count = 0
       private_count = 0
       Tap.each do |tap|
         tap_count += 1
         formula_count += tap.formula_files.size
         command_count += tap.command_files.size
-        pinned_count += 1 if tap.pinned?
         private_count += 1 if tap.private?
       end
       info = "#{tap_count} #{"tap".pluralize(tap_count)}"
-      info += ", #{pinned_count} pinned"
       info += ", #{private_count} private"
       info += ", #{formula_count} #{"formula".pluralize(formula_count)}"
       info += ", #{command_count} #{"command".pluralize(command_count)}"
diff --git a/Library/Homebrew/formulary.rb b/Library/Homebrew/formulary.rb
index 0aee5e3d6a..ee45ee0faa 100644
--- a/Library/Homebrew/formulary.rb
+++ b/Library/Homebrew/formulary.rb
@@ -516,15 +516,14 @@ module Formulary
     def formula_name_path(tapped_name, warn: true)
       user, repo, name = tapped_name.split("/", 3).map(&:downcase)
       @tap = Tap.fetch user, repo
-      formula_dir = @tap.formula_dir || @tap.path
-      path = formula_dir/"#{name}.rb"
+      path = find_formula_from_name(name)
 
       unless path.file?
         if (possible_alias = @tap.alias_dir/name).file?
           path = possible_alias.resolved_path
           name = path.basename(".rb").to_s
         elsif (new_name = @tap.formula_renames[name]) &&
-              (new_path = formula_dir/"#{new_name}.rb").file?
+              (new_path = find_formula_from_name(new_name)).file?
           old_name = name
           path = new_path
           name = new_name
@@ -562,6 +561,12 @@ module Formulary
       e.issues_url = tap.issues_url || tap.to_s
       raise
     end
+
+    private
+
+    def find_formula_from_name(name)
+      Formulary.find_formula_in_tap(name, @tap)
+    end
   end
 
   # Pseudo-loader which will raise a {FormulaUnavailableError} when trying to load the corresponding formula.
@@ -800,22 +805,28 @@ module Formulary
   end
 
   def self.core_path(name)
-    CoreTap.instance.formula_dir/"#{name.to_s.downcase}.rb"
+    find_formula_in_tap(name.to_s.downcase, CoreTap.instance)
   end
 
   def self.core_alias_path(name)
     CoreTap.instance.alias_dir/name.to_s.downcase
   end
 
-  def self.tap_paths(name, taps = Dir[HOMEBREW_LIBRARY/"Taps/*/*/"])
+  def self.tap_paths(name, taps = Tap)
     name = name.to_s.downcase
     taps.map do |tap|
-      Pathname.glob([
-        "#{tap}Formula/#{name}.rb",
-        "#{tap}HomebrewFormula/#{name}.rb",
-        "#{tap}#{name}.rb",
-        "#{tap}Aliases/#{name}",
-      ]).find(&:file?)
-    end.compact
+      formula_path = find_formula_in_tap(name, tap)
+
+      alias_path = tap.alias_dir/name
+      next alias_path if !formula_path.exist? && alias_path.exist?
+
+      formula_path
+    end.select(&:file?)
+  end
+
+  def self.find_formula_in_tap(name, tap)
+    filename = "#{name}.rb"
+
+    Tap.formula_files_by_name(tap).fetch(filename, tap.formula_dir/filename)
   end
 end
diff --git a/Library/Homebrew/tap.rb b/Library/Homebrew/tap.rb
index cc70e67acf..8024e2e112 100644
--- a/Library/Homebrew/tap.rb
+++ b/Library/Homebrew/tap.rb
@@ -1,4 +1,4 @@
-# typed: false
+# typed: true
 # frozen_string_literal: true
 
 require "commands"
@@ -416,7 +416,6 @@ class Tap
     abv = path.abv
     formatted_contents = contents.presence&.to_sentence&.dup&.prepend(" ")
 
-    unpin if pinned?
     CacheStoreDatabase.use(:descriptions) do |db|
       DescriptionCacheStore.new(db)
                            .delete_from_formula_names!(formula_names)
@@ -451,15 +450,23 @@ class Tap
   end
 
   # Path to the directory of all {Formula} files for this {Tap}.
+  sig { returns(Pathname) }
   def formula_dir
-    @formula_dir ||= potential_formula_dirs.find(&:directory?) || (path/"Formula")
+    # Official formulae taps always use this directory, saves time to hardcode.
+    @formula_dir ||= if official?
+      path/"Formula"
+    else
+      potential_formula_dirs.find(&:directory?) || (path/"Formula")
+    end
   end
 
+  sig { returns(T::Array[Pathname]) }
   def potential_formula_dirs
     @potential_formula_dirs ||= [path/"Formula", path/"HomebrewFormula", path].freeze
   end
 
   # Path to the directory of all {Cask} files for this {Tap}.
+  sig { returns(Pathname) }
   def cask_dir
     @cask_dir ||= path/"Casks"
   end
@@ -483,15 +490,35 @@ class Tap
   end
 
   # An array of all {Formula} files of this {Tap}.
+  sig { returns(T::Array[Pathname]) }
   def formula_files
     @formula_files ||= if formula_dir.directory?
-      formula_dir.children.select(&method(:ruby_file?))
+      # TODO: odeprecate the non-official/old logic with a new minor release somehow?
+      if official?
+        formula_dir.find
+      else
+        formula_dir.children
+      end.select(&method(:ruby_file?))
     else
       []
     end
   end
 
+  # A cached hash of {Formula} basenames to {Formula} file pathnames for a {Tap}
+  sig { params(tap: Tap).returns(T::Hash[String, Pathname]) }
+  def self.formula_files_by_name(tap)
+    cache_key = "formula_files_by_name_#{tap}"
+    cache.fetch(cache_key) do |key|
+      cache[key] = tap.formula_files.each_with_object({}) do |file, hash|
+        # If there's more than one file with the same basename: intentionally
+        # ignore the later ones here.
+        hash[file.basename.to_s] ||= file
+      end
+    end
+  end
+
   # An array of all versioned {Formula} files of this {Tap}.
+  sig { returns(T::Array[Pathname]) }
   def versioned_formula_files
     @versioned_formula_files ||= formula_files.select do |file|
       file.basename(".rb").to_s =~ /@[\d.]+$/
@@ -499,16 +526,37 @@ class Tap
   end
 
   # An array of all {Cask} files of this {Tap}.
+  sig { returns(T::Array[Pathname]) }
   def cask_files
     @cask_files ||= if cask_dir.directory?
-      cask_dir.children.select(&method(:ruby_file?))
+      # TODO: odeprecate the non-official/old logic with a new minor release somehow?
+      if official?
+        cask_dir.find
+      else
+        cask_dir.children
+      end.select(&method(:ruby_file?))
     else
       []
     end
   end
 
+  # A cached hash of {Cask} basenames to {Cask} file pathnames for a {Tap}
+  sig { params(tap: Tap).returns(T::Hash[String, Pathname]) }
+  def self.cask_files_by_name(tap)
+    cache_key = "cask_files_by_name_#{tap}"
+
+    cache.fetch(cache_key) do |key|
+      cache[key] = tap.cask_files.each_with_object({}) do |file, hash|
+        # If there's more than one file with the same basename: intentionally
+        # ignore the later ones here.
+        hash[file.basename.to_s] ||= file
+      end
+    end
+  end
+
   # returns true if the file has a Ruby extension
   # @private
+  sig { params(file: Pathname).returns(T::Boolean) }
   def ruby_file?(file)
     file.extname == ".rb"
   end
@@ -516,45 +564,56 @@ class Tap
   # return true if given path would present a {Formula} file in this {Tap}.
   # accepts both absolute path and relative path (relative to this {Tap}'s path)
   # @private
+  sig { params(file: T.any(String, Pathname)).returns(T::Boolean) }
   def formula_file?(file)
     file = Pathname.new(file) unless file.is_a? Pathname
     file = file.expand_path(path)
-    ruby_file?(file) && file.parent == formula_dir
+    return false unless ruby_file?(file)
+
+    file.to_s.start_with?("#{formula_dir}/")
   end
 
   # return true if given path would present a {Cask} file in this {Tap}.
   # accepts both absolute path and relative path (relative to this {Tap}'s path)
   # @private
+  sig { params(file: T.any(String, Pathname)).returns(T::Boolean) }
   def cask_file?(file)
     file = Pathname.new(file) unless file.is_a? Pathname
     file = file.expand_path(path)
-    ruby_file?(file) && file.parent == cask_dir
+    return false unless ruby_file?(file)
+
+    file.to_s.start_with?("#{cask_dir}/")
   end
 
   # An array of all {Formula} names of this {Tap}.
+  sig { returns(T::Array[String]) }
   def formula_names
     @formula_names ||= formula_files.map(&method(:formula_file_to_name))
   end
 
   # An array of all {Cask} tokens of this {Tap}.
+  sig { returns(T::Array[String]) }
   def cask_tokens
     @cask_tokens ||= cask_files.map(&method(:formula_file_to_name))
   end
 
   # path to the directory of all alias files for this {Tap}.
   # @private
+  sig { returns(Pathname) }
   def alias_dir
     @alias_dir ||= path/"Aliases"
   end
 
   # an array of all alias files of this {Tap}.
   # @private
+  sig { returns(T::Array[Pathname]) }
   def alias_files
     @alias_files ||= Pathname.glob("#{alias_dir}/*").select(&:file?)
   end
 
   # an array of all aliases of this {Tap}.
   # @private
+  sig { returns(T::Array[String]) }
   def aliases
     @aliases ||= alias_files.map { |f| alias_file_to_name(f) }
   end
@@ -584,11 +643,13 @@ class Tap
     @alias_reverse_table
   end
 
+  sig { returns(Pathname) }
   def command_dir
     @command_dir ||= path/"cmd"
   end
 
   # An array of all commands files of this {Tap}.
+  sig { returns(T::Array[Pathname]) }
   def command_files
     @command_files ||= if command_dir.directory?
       Commands.find_commands(command_dir)
@@ -597,19 +658,7 @@ class Tap
     end
   end
 
-  # path to the pin record for this {Tap}.
-  # @private
-  def pinned_symlink_path
-    HOMEBREW_LIBRARY/"PinnedTaps/#{name}"
-  end
-
-  # True if this {Tap} has been pinned.
-  def pinned?
-    return @pinned if instance_variable_defined?(:@pinned)
-
-    @pinned = pinned_symlink_path.directory?
-  end
-
+  sig { returns(Hash) }
   def to_hash
     hash = {
       "name"          => name,
@@ -635,6 +684,7 @@ class Tap
   end
 
   # Hash with tap formula renames.
+  sig { returns(Hash) }
   def formula_renames
     @formula_renames ||= if (rename_file = path/HOMEBREW_TAP_FORMULA_RENAMES_FILE).file?
       JSON.parse(rename_file.read)
@@ -644,6 +694,7 @@ class Tap
   end
 
   # Hash with tap migrations.
+  sig { returns(Hash) }
   def tap_migrations
     @tap_migrations ||= if (migration_file = path/HOMEBREW_TAP_MIGRATIONS_FILE).file?
       JSON.parse(migration_file.read)
@@ -665,18 +716,19 @@ class Tap
   end
 
   # Hash with pypi formula mappings
-  sig { returns(Hash) }
   def pypi_formula_mappings
     @pypi_formula_mappings = read_formula_list path/HOMEBREW_TAP_PYPI_FORMULA_MAPPINGS
   end
 
   # @private
+  sig { returns(T::Boolean) }
   def should_report_analytics?
     return Homebrew::EnvConfig.install_from_api? && official? unless installed?
 
     !private?
   end
 
+  sig { params(other: T.nilable(T.any(String, Tap))).returns(T::Boolean) }
   def ==(other)
     other = Tap.fetch(other) if other.is_a?(String)
     self.class == other.class && name == other.name
@@ -695,6 +747,7 @@ class Tap
   end
 
   # An array of all installed {Tap} names.
+  sig { returns(T::Array[String]) }
   def self.names
     map(&:name).sort
   end
@@ -712,11 +765,13 @@ class Tap
   end
 
   # @private
+  sig { params(file: Pathname).returns(String) }
   def formula_file_to_name(file)
     "#{name}/#{file.basename(".rb")}"
   end
 
   # @private
+  sig { params(file: Pathname).returns(String) }
   def alias_file_to_name(file)
     "#{name}/#{file.basename}"
   end
@@ -796,10 +851,12 @@ class CoreTap < Tap
     super "Homebrew", "core"
   end
 
+  sig { returns(CoreTap) }
   def self.instance
     @instance ||= new
   end
 
+  sig { void }
   def self.ensure_installed!
     return if instance.installed?
     return if Homebrew::EnvConfig.install_from_api?
@@ -811,6 +868,7 @@ class CoreTap < Tap
     instance.install
   end
 
+  sig { returns(String) }
   def remote
     super if installed? || !Homebrew::EnvConfig.install_from_api?
 
@@ -840,24 +898,6 @@ class CoreTap < Tap
     super
   end
 
-  # @private
-  sig { void }
-  def pin
-    raise "Tap#pin is not available for CoreTap"
-  end
-
-  # @private
-  sig { void }
-  def unpin
-    raise "Tap#unpin is not available for CoreTap"
-  end
-
-  # @private
-  sig { returns(T::Boolean) }
-  def pinned?
-    false
-  end
-
   # @private
   sig { returns(T::Boolean) }
   def core_tap?
@@ -871,6 +911,7 @@ class CoreTap < Tap
   end
 
   # @private
+  sig { returns(Pathname) }
   def formula_dir
     @formula_dir ||= begin
       self.class.ensure_installed!
@@ -879,6 +920,7 @@ class CoreTap < Tap
   end
 
   # @private
+  sig { returns(Pathname) }
   def alias_dir
     @alias_dir ||= begin
       self.class.ensure_installed!
@@ -887,6 +929,7 @@ class CoreTap < Tap
   end
 
   # @private
+  sig { returns(Hash) }
   def formula_renames
     @formula_renames ||= begin
       self.class.ensure_installed!
@@ -895,6 +938,7 @@ class CoreTap < Tap
   end
 
   # @private
+  sig { returns(Hash) }
   def tap_migrations
     @tap_migrations ||= begin
       self.class.ensure_installed!
@@ -903,6 +947,7 @@ class CoreTap < Tap
   end
 
   # @private
+  sig { returns(Hash) }
   def audit_exceptions
     @audit_exceptions ||= begin
       self.class.ensure_installed!
@@ -911,6 +956,7 @@ class CoreTap < Tap
   end
 
   # @private
+  sig { returns(Hash) }
   def style_exceptions
     @style_exceptions ||= begin
       self.class.ensure_installed!
@@ -919,6 +965,7 @@ class CoreTap < Tap
   end
 
   # @private
+  sig { returns(Hash) }
   def pypi_formula_mappings
     @pypi_formula_mappings ||= begin
       self.class.ensure_installed!
@@ -927,16 +974,19 @@ class CoreTap < Tap
   end
 
   # @private
+  sig { params(file: Pathname).returns(String) }
   def formula_file_to_name(file)
     file.basename(".rb").to_s
   end
 
   # @private
+  sig { params(file: Pathname).returns(String) }
   def alias_file_to_name(file)
     file.basename.to_s
   end
 
   # @private
+  sig { returns(T::Array[String]) }
   def aliases
     return super if installed? || !Homebrew::EnvConfig.install_from_api?
 
@@ -944,6 +994,7 @@ class CoreTap < Tap
   end
 
   # @private
+  sig { returns(T::Array[String]) }
   def formula_names
     return super if installed? || !Homebrew::EnvConfig.install_from_api?
 
@@ -953,8 +1004,11 @@ end
 
 # Permanent configuration per {Tap} using `git-config(1)`.
 class TapConfig
+  extend T::Sig
+
   attr_reader :tap
 
+  sig { params(tap: Tap).void }
   def initialize(tap)
     @tap = tap
   end
diff --git a/Library/Homebrew/test/cask/cask_loader/from__path_loader_spec.rb b/Library/Homebrew/test/cask/cask_loader/from_path_loader_spec.rb
similarity index 100%
rename from Library/Homebrew/test/cask/cask_loader/from__path_loader_spec.rb
rename to Library/Homebrew/test/cask/cask_loader/from_path_loader_spec.rb
diff --git a/Library/Homebrew/test/cask/cask_loader/from_tap_loader_spec.rb b/Library/Homebrew/test/cask/cask_loader/from_tap_loader_spec.rb
new file mode 100644
index 0000000000..4d077cdc8d
--- /dev/null
+++ b/Library/Homebrew/test/cask/cask_loader/from_tap_loader_spec.rb
@@ -0,0 +1,35 @@
+# typed: false
+# frozen_string_literal: true
+
+describe Cask::CaskLoader::FromTapLoader do
+  let(:cask_name) { "testball" }
+  let(:cask_full_name) { "homebrew/cask/#{cask_name}" }
+  let(:cask_path) { Tap.default_cask_tap.cask_dir/"#{cask_name}.rb" }
+
+  describe "#load" do
+    before do
+      cask_path.parent.mkpath
+      cask_path.write <<~RUBY
+        cask '#{cask_name}' do
+          url 'https://brew.sh/'
+        end
+      RUBY
+    end
+
+    it "returns a Cask" do
+      expect(described_class.new(cask_full_name).load(config: nil)).to be_a(Cask::Cask)
+    end
+
+    it "raises an error if the Cask cannot be found" do
+      expect { described_class.new("foo/bar/baz").load(config: nil) }.to raise_error(Cask::CaskUnavailableError)
+    end
+
+    context "with sharded Cask directory" do
+      let(:cask_path) { Tap.default_cask_tap.cask_dir/cask_name[0]/"#{cask_name}.rb" }
+
+      it "returns a Cask" do
+        expect(described_class.new(cask_full_name).load(config: nil)).to be_a(Cask::Cask)
+      end
+    end
+  end
+end
diff --git a/Library/Homebrew/test/formulary_spec.rb b/Library/Homebrew/test/formulary_spec.rb
index 910931c86f..1aa1956539 100644
--- a/Library/Homebrew/test/formulary_spec.rb
+++ b/Library/Homebrew/test/formulary_spec.rb
@@ -81,6 +81,21 @@ describe Formulary do
       }.to raise_error(ArgumentError)
     end
 
+    context "with sharded Formula directory" do
+      before { CoreTap.instance.clear_cache }
+
+      let(:formula_name) { "testball_sharded" }
+      let(:formula_path) { CoreTap.new.formula_dir/formula_name[0]/"#{formula_name}.rb" }
+
+      it "returns a Formula" do
+        expect(described_class.factory(formula_name)).to be_a(Formula)
+      end
+
+      it "returns a Formula when given a fully qualified name" do
+        expect(described_class.factory("homebrew/core/#{formula_name}")).to be_a(Formula)
+      end
+    end
+
     context "when the Formula has the wrong class" do
       let(:formula_name) { "giraffe" }
       let(:formula_content) do
@@ -171,7 +186,7 @@ describe Formulary do
     context "when loading from Tap" do
       let(:tap) { Tap.new("homebrew", "foo") }
       let(:another_tap) { Tap.new("homebrew", "bar") }
-      let(:formula_path) { tap.path/"#{formula_name}.rb" }
+      let(:formula_path) { tap.path/"Formula/#{formula_name}.rb" }
 
       it "returns a Formula when given a name" do
         expect(described_class.factory(formula_name)).to be_a(Formula)
@@ -195,8 +210,8 @@ describe Formulary do
       end
 
       it "raises an error if a Formula is in multiple Taps" do
-        another_tap.path.mkpath
-        (another_tap.path/"#{formula_name}.rb").write formula_content
+        (another_tap.path/"Formula").mkpath
+        (another_tap.path/"Formula/#{formula_name}.rb").write formula_content
 
         expect {
           described_class.factory(formula_name)
diff --git a/Library/Homebrew/test/missing_formula_spec.rb b/Library/Homebrew/test/missing_formula_spec.rb
index d93851f460..84e96336bd 100644
--- a/Library/Homebrew/test/missing_formula_spec.rb
+++ b/Library/Homebrew/test/missing_formula_spec.rb
@@ -61,8 +61,8 @@ describe Homebrew::MissingFormula do
 
     before do
       tap_path = Tap::TAP_DIRECTORY/"homebrew/homebrew-foo"
-      tap_path.mkpath
-      (tap_path/"deleted-formula.rb").write "placeholder"
+      (tap_path/"Formula").mkpath
+      (tap_path/"Formula/deleted-formula.rb").write "placeholder"
       ENV.delete "GIT_AUTHOR_DATE"
       ENV.delete "GIT_COMMITTER_DATE"
 
@@ -70,7 +70,7 @@ describe Homebrew::MissingFormula do
         system "git", "init"
         system "git", "add", "--all"
         system "git", "commit", "-m", "initial state"
-        system "git", "rm", "deleted-formula.rb"
+        system "git", "rm", "Formula/deleted-formula.rb"
         system "git", "commit", "-m", "delete formula 'deleted-formula'"
       end
     end
diff --git a/Library/Homebrew/test/tap_spec.rb b/Library/Homebrew/test/tap_spec.rb
index b13ee778b3..3850652ec2 100644
--- a/Library/Homebrew/test/tap_spec.rb
+++ b/Library/Homebrew/test/tap_spec.rb
@@ -528,15 +528,12 @@ describe Tap do
       expect(core_tap.name).to eq("homebrew/core")
       expect(core_tap.command_files).to eq([])
       expect(core_tap).to be_installed
-      expect(core_tap).not_to be_pinned
       expect(core_tap).to be_official
       expect(core_tap).to be_a_core_tap
     end
 
     specify "forbidden operations" do
       expect { core_tap.uninstall }.to raise_error(RuntimeError)
-      expect { core_tap.pin }.to raise_error(RuntimeError)
-      expect { core_tap.unpin }.to raise_error(RuntimeError)
     end
 
     specify "files" do