diff --git a/Library/Homebrew/cask/download.rb b/Library/Homebrew/cask/download.rb
index 5d577eeb2e..e2f43bf526 100644
--- a/Library/Homebrew/cask/download.rb
+++ b/Library/Homebrew/cask/download.rb
@@ -40,6 +40,10 @@ module Cask
       end
     end
 
+    def time_file_size
+      downloader.resolved_time_file_size
+    end
+
     def clear_cache
       downloader.clear_cache
     end
diff --git a/Library/Homebrew/cask/installer.rb b/Library/Homebrew/cask/installer.rb
index c93530edec..a3cf058dec 100644
--- a/Library/Homebrew/cask/installer.rb
+++ b/Library/Homebrew/cask/installer.rb
@@ -30,7 +30,8 @@ module Cask
     def initialize(cask, command: SystemCommand, force: false,
                    skip_cask_deps: false, binaries: true, verbose: false,
                    require_sha: false, upgrade: false,
-                   installed_as_dependency: false, quarantine: true)
+                   installed_as_dependency: false, quarantine: true,
+                   verify_download_integrity: true)
       @cask = cask
       @command = command
       @force = force
@@ -42,6 +43,7 @@ module Cask
       @upgrade = upgrade
       @installed_as_dependency = installed_as_dependency
       @quarantine = quarantine
+      @verify_download_integrity = verify_download_integrity
     end
 
     attr_predicate :binaries?, :force?, :skip_cask_deps?, :require_sha?,
@@ -150,13 +152,10 @@ module Cask
       s.freeze
     end
 
+    sig { returns(Pathname) }
     def download
-      return @downloaded_path if @downloaded_path
-
-      odebug "Downloading"
-      @downloaded_path = Download.new(@cask, quarantine: quarantine?).fetch
-      odebug "Downloaded to -> #{@downloaded_path}"
-      @downloaded_path
+      @download ||= Download.new(@cask, quarantine: quarantine?)
+                            .fetch(verify_download_integrity: @verify_download_integrity)
     end
 
     def verify_has_sha
@@ -171,15 +170,15 @@ module Cask
 
     def primary_container
       @primary_container ||= begin
-        download
-        UnpackStrategy.detect(@downloaded_path, type: @cask.container&.type, merge_xattrs: true)
+        downloaded_path = download
+        UnpackStrategy.detect(downloaded_path, type: @cask.container&.type, merge_xattrs: true)
       end
     end
 
-    def extract_primary_container
+    def extract_primary_container(to: @cask.staged_path)
       odebug "Extracting primary container"
 
-      odebug "Using container class #{primary_container.class} for #{@downloaded_path}"
+      odebug "Using container class #{primary_container.class} for #{primary_container.path}"
 
       basename = CGI.unescape(File.basename(@cask.url.path))
 
@@ -191,16 +190,16 @@ module Cask
           FileUtils.chmod_R "+rw", tmpdir/nested_container, force: true, verbose: verbose?
 
           UnpackStrategy.detect(tmpdir/nested_container, merge_xattrs: true)
-                        .extract_nestedly(to: @cask.staged_path, verbose: verbose?)
+                        .extract_nestedly(to: to, verbose: verbose?)
         end
       else
-        primary_container.extract_nestedly(to: @cask.staged_path, basename: basename, verbose: verbose?)
+        primary_container.extract_nestedly(to: to, basename: basename, verbose: verbose?)
       end
 
       return unless quarantine?
       return unless Quarantine.available?
 
-      Quarantine.propagate(from: @downloaded_path, to: @cask.staged_path)
+      Quarantine.propagate(from: primary_container.path, to: to)
     end
 
     def install_artifacts
diff --git a/Library/Homebrew/dev-cmd/bump-cask-pr.rb b/Library/Homebrew/dev-cmd/bump-cask-pr.rb
index 7a4b74e6bb..b5752c6fa1 100644
--- a/Library/Homebrew/dev-cmd/bump-cask-pr.rb
+++ b/Library/Homebrew/dev-cmd/bump-cask-pr.rb
@@ -72,9 +72,10 @@ module Homebrew
     new_version = Cask::DSL::Version.new(new_version)
     new_base_url = args.url
     new_hash = args.sha256
+    new_hash = :no_check if new_hash == ":no_check"
 
     old_version = cask.version
-    old_hash = cask.sha256.to_s
+    old_hash = cask.sha256
 
     tap_full_name = cask.tap&.full_name
     default_remote_branch = cask.tap.path.git_origin_branch if cask.tap
@@ -95,7 +96,7 @@ module Homebrew
     elsif old_version.latest?
       opoo "No --url= argument specified!" unless new_base_url
     elsif new_version.latest?
-      opoo "Ignoring specified --sha256= argument." if new_hash
+      opoo "Ignoring specified --sha256= argument." if new_hash && new_check != :no_check
     elsif Version.new(new_version) < Version.new(old_version)
       odie <<~EOS
         You need to bump this cask manually since changing the
@@ -136,7 +137,9 @@ module Homebrew
       ]
     end
 
-    if !new_version.latest? && (new_hash.nil? || cask.languages.present?)
+    if new_version.latest?
+      new_hash = :no_check
+    elsif new_hash.nil? || cask.languages.present?
       tmp_contents = Utils::Inreplace.inreplace_pairs(cask.sourcefile_path,
                                                       replacement_pairs.uniq.compact,
                                                       read_only_run: true,
@@ -172,15 +175,14 @@ module Homebrew
       end
     end
 
-    replacement_pairs << if old_version.latest?
+    p old_hash
+
+    replacement_pairs << if old_version.latest? || new_version.latest? || new_hash == :no_check
+      hash_regex = old_hash == :no_check ? ":no_check" : "[\"']#{Regexp.escape(old_hash.to_s)}[\"']"
+
       [
-        "sha256 :no_check",
-        "sha256 \"#{new_hash}\"",
-      ]
-    elsif new_version.latest?
-      [
-        "sha256 \"#{old_hash}\"",
-        "sha256 :no_check",
+        /sha256\s+#{hash_regex}/m,
+        "sha256 #{new_hash == :no_check ? ":no_check" : "\"#{new_hash}\""}",
       ]
     else
       [
diff --git a/Library/Homebrew/dev-cmd/bump-unversioned-casks.rb b/Library/Homebrew/dev-cmd/bump-unversioned-casks.rb
new file mode 100644
index 0000000000..435bcc08d8
--- /dev/null
+++ b/Library/Homebrew/dev-cmd/bump-unversioned-casks.rb
@@ -0,0 +1,201 @@
+# typed: false
+# frozen_string_literal: true
+
+require "cask/download"
+require "cask/installer"
+require "cask/cask_loader"
+require "cli/parser"
+require "tap"
+
+module Homebrew
+  extend T::Sig
+
+  extend SystemCommand::Mixin
+
+  sig { returns(CLI::Parser) }
+  def self.bump_unversioned_casks_args
+    Homebrew::CLI::Parser.new do
+      usage_banner <<~EOS
+        `bump-unversioned-casks` [<options>] [<tap>]
+
+        Check all casks with unversioned URLs in a given <tap> for updates.
+      EOS
+      switch "-n", "--dry-run",
+             description: "List what would be done, but do not actually do anything."
+      flag  "--limit=",
+            description: "Maximum number of casks to update."
+      flag   "--state-file=",
+             description: "File for keeping track of state."
+
+      named 1
+    end
+  end
+
+  sig { void }
+  def self.bump_unversioned_casks
+    args = bump_unversioned_casks_args.parse
+
+    state_file = if args.state_file.present?
+      Pathname(args.state_file).expand_path
+    else
+      HOMEBREW_CACHE/"bump_unversioned_casks.json"
+    end
+    state_file.dirname.mkpath
+
+    tap = Tap.fetch(args.named.first)
+
+    old_state = state_file.exist? ? JSON.parse(state_file.read) : {}
+
+    new_state = {}
+
+    cask_files = tap.cask_files
+    unversioned_cask_files = cask_files.select do |cask_file|
+      url = cask_file.each_line do |line|
+        url = line[/\s*url\s+"([^"]+)"\s*/, 1]
+        break url if url
+      end
+
+      url.present? && url.exclude?('#{')
+    end.sort
+
+    unversioned_casks = unversioned_cask_files.map { |path| Cask::CaskLoader.load(path) }
+
+    ohai "Static Casks:"
+    puts "Total:      #{unversioned_casks.count}"
+    puts "Single-App: #{unversioned_casks.count { |c| single_app_cask?(c) }}"
+    puts "Single-Pkg: #{unversioned_casks.count { |c| single_pkg_cask?(c) }}"
+
+    limit = args.limit.presence&.to_i || unversioned_casks.count
+
+    unversioned_casks.shuffle.each do |cask|
+      ohai "Checking #{cask.full_name}"
+
+      unless single_app_cask?(cask)
+        opoo "Skipping, not a single-app cask."
+        next
+      end
+
+      download = Cask::Download.new(cask)
+      time, file_size = begin
+        download.time_file_size
+      rescue
+        opoo "Skipping, cannot get time and file size."
+        next
+      end
+
+      odebug "Time: #{time.inspect}"
+      odebug "Size: #{file_size.inspect}"
+
+      last_state = old_state.fetch(cask.full_name, {})
+      last_check_time = last_state["check_time"]&.yield_self { |t| Time.parse(t) }
+
+      check_time = Time.now
+      if last_check_time && check_time < (last_check_time + 1.day)
+        opoo "Skipping, already checked within the last 24 hours."
+        next
+      end
+
+      last_sha256 = last_state["sha256"]
+      last_time = last_state["time"]&.yield_self { |t| Time.parse(t) }
+      last_file_size = last_state["file_size"]
+
+      next if last_time == time && last_file_size == file_size
+
+      installer = Cask::Installer.new(cask, verify_download_integrity: false)
+
+      begin
+        cached_download = installer.download
+      rescue => e
+        onoe e
+        next
+      end
+
+      sha256 = cached_download.sha256
+
+      if last_sha256 != sha256 && (version = guess_cask_version(cask, installer))
+        odebug "Version: #{version.inspect}"
+
+        if cask.version == version
+          oh1 "Cask #{cask} is up-to-date at #{version}"
+        else
+          bump_cask_pr_args = [
+            "bump-cask-pr",
+            "--version", version.to_s,
+            "--sha256", ":no_check",
+            "--message", "Automatic update via `brew bump-unversioned-casks`.",
+            cask.sourcefile_path
+          ]
+
+          if args.dry_run?
+            bump_cask_pr_args << "--dry-run"
+            oh1 "Would bump #{cask} from #{cask.version} to #{version}"
+          else
+            oh1 "Bumping #{cask} from #{cask.version} to #{version}"
+          end
+
+          begin
+            system_command! HOMEBREW_BREW_FILE, args: bump_cask_pr_args
+          rescue ErrorDuringExecution => e
+            onoe e
+            Homebrew.failed = true
+          end
+        end
+      end
+
+      unless args.dry_run?
+        new_state[cask.full_name] = {
+          "sha256"     => sha256,
+          "check_time" => check_time.iso8601,
+          "time"       => time&.iso8601,
+          "file_size"  => file_size,
+        }
+      end
+
+      break if (limit -= 1).zero?
+    end
+
+    state_file.atomic_write JSON.pretty_generate(old_state.merge(new_state))
+  end
+
+  sig { params(cask: Cask::Cask, installer: Cask::Installer).returns(T.nilable(String)) }
+  def self.guess_cask_version(cask, installer)
+    apps = cask.artifacts.select { |a| a.is_a?(Cask::Artifact::App) }
+    return if apps.count != 1
+
+    Dir.mktmpdir do |dir|
+      dir = Pathname(dir)
+
+      installer.extract_primary_container(to: dir)
+
+      plists = apps.flat_map do |app|
+        Pathname.glob(dir/"**"/app.source.basename/"Contents"/"Info.plist")
+      end
+      next if plists.empty?
+
+      plist = plists.first
+
+      system_command! "plutil", args: ["-convert", "xml1", plist]
+      plist = Plist.parse_xml(plist.read)
+
+      short_version = plist["CFBundleShortVersionString"]
+      version = plist["CFBundleVersion"]
+
+      return "#{short_version},#{version}" if cask.version.include?(",")
+
+      return cask.version.to_s if [short_version, version].include?(cask.version.to_s)
+
+      return short_version if short_version&.match(/\A\d+(\.\d+)+\Z/)
+      return version if version&.match(/\A\d+(\.\d+)+\Z/)
+
+      short_version || version
+    end
+  end
+
+  def self.single_app_cask?(cask)
+    cask.artifacts.count { |a| a.is_a?(Cask::Artifact::App) } == 1
+  end
+
+  def self.single_pkg_cask?(cask)
+    cask.artifacts.count { |a| a.is_a?(Cask::Artifact::Pkg) } == 1
+  end
+end
diff --git a/Library/Homebrew/download_strategy.rb b/Library/Homebrew/download_strategy.rb
index a2deeed57f..b33ec75036 100644
--- a/Library/Homebrew/download_strategy.rb
+++ b/Library/Homebrew/download_strategy.rb
@@ -356,7 +356,7 @@ class CurlDownloadStrategy < AbstractFileDownloadStrategy
 
       ohai "Downloading #{url}"
 
-      resolved_url, _, url_time = resolve_url_basename_time(url)
+      resolved_url, _, url_time, = resolve_url_basename_time_file_size(url)
 
       fresh = if cached_location.exist? && url_time
         url_time <= cached_location.mtime
@@ -398,14 +398,19 @@ class CurlDownloadStrategy < AbstractFileDownloadStrategy
     rm_rf(temporary_path)
   end
 
+  def resolved_time_file_size
+    _, _, time, file_size = resolve_url_basename_time_file_size(url)
+    [time, file_size]
+  end
+
   private
 
   def resolved_url_and_basename
-    resolved_url, basename, = resolve_url_basename_time(url)
+    resolved_url, basename, = resolve_url_basename_time_file_size(url)
     [resolved_url, basename]
   end
 
-  def resolve_url_basename_time(url)
+  def resolve_url_basename_time_file_size(url)
     @resolved_info_cache ||= {}
     return @resolved_info_cache[url] if @resolved_info_cache.include?(url)
 
@@ -458,9 +463,15 @@ class CurlDownloadStrategy < AbstractFileDownloadStrategy
            .map { |t| t.match?(/^\d+$/) ? Time.at(t.to_i) : Time.parse(t) }
            .last
 
+    file_size =
+      lines.map { |line| line[/^Content-Length:\s*(\d+)/i, 1] }
+           .compact
+           .map(&:to_i)
+           .last
+
     basename = filenames.last || parse_basename(redirect_url)
 
-    @resolved_info_cache[url] = [redirect_url, basename, time]
+    @resolved_info_cache[url] = [redirect_url, basename, time, file_size]
   end
 
   def _fetch(url:, resolved_url:)
@@ -526,7 +537,7 @@ class CurlApacheMirrorDownloadStrategy < CurlDownloadStrategy
     @combined_mirrors = [*@mirrors, *backup_mirrors]
   end
 
-  def resolve_url_basename_time(url)
+  def resolve_url_basename_time_file_size(url)
     if url == self.url
       super("#{apache_mirrors["preferred"]}#{apache_mirrors["path_info"]}")
     else
diff --git a/Library/Homebrew/utils/github.rb b/Library/Homebrew/utils/github.rb
index c589748168..c3c493231a 100644
--- a/Library/Homebrew/utils/github.rb
+++ b/Library/Homebrew/utils/github.rb
@@ -736,11 +736,12 @@ module GitHub
         EOS
         user_message = args.message
         if user_message
-          pr_message += <<~EOS
+          pr_message = <<~EOS
+            #{user_message}
 
             ---
 
-            #{user_message}
+            #{pr_message}
           EOS
         end
 
diff --git a/completions/internal_commands_list.txt b/completions/internal_commands_list.txt
index f2c3de6ba2..c9c4fbf6aa 100644
--- a/completions/internal_commands_list.txt
+++ b/completions/internal_commands_list.txt
@@ -18,6 +18,7 @@ bump
 bump-cask-pr
 bump-formula-pr
 bump-revision
+bump-unversioned-casks
 cask
 cat
 cleanup
diff --git a/docs/Manpage.md b/docs/Manpage.md
index 27525453db..78c55fbbdc 100644
--- a/docs/Manpage.md
+++ b/docs/Manpage.md
@@ -899,6 +899,17 @@ present, "revision 1" will be added.
 * `--message`:
   Append *`message`* to the default commit message.
 
+### `bump-unversioned-casks` [*`options`*] [*`tap`*]
+
+Check all casks with unversioned URLs in a given *`tap`* for updates.
+
+* `-n`, `--dry-run`:
+  List what would be done, but do not actually do anything.
+* `--limit`:
+  Maximum number of casks to update.
+* `--state-file`:
+  File for keeping track of state.
+
 ### `cat` *`formula`*|*`cask`*
 
 Display the source of a *`formula`* or *`cask`*.
diff --git a/manpages/brew.1 b/manpages/brew.1
index 2e6304a461..6da1f9c037 100644
--- a/manpages/brew.1
+++ b/manpages/brew.1
@@ -1245,6 +1245,21 @@ Print what would be done rather than doing it\.
 \fB\-\-message\fR
 Append \fImessage\fR to the default commit message\.
 .
+.SS "\fBbump\-unversioned\-casks\fR [\fIoptions\fR] [\fItap\fR]"
+Check all casks with unversioned URLs in a given \fItap\fR for updates\.
+.
+.TP
+\fB\-n\fR, \fB\-\-dry\-run\fR
+List what would be done, but do not actually do anything\.
+.
+.TP
+\fB\-\-limit\fR
+Maximum number of casks to update\.
+.
+.TP
+\fB\-\-state\-file\fR
+File for keeping track of state\.
+.
 .SS "\fBcat\fR \fIformula\fR|\fIcask\fR"
 Display the source of a \fIformula\fR or \fIcask\fR\.
 .