This is what I came up with:

#!/bin/env ruby

exit if ARGV[0].nil?
exit unless File.exists?(ARGV[0])

CACHE_DIR_NAME='cache'

haml_file = ARGV[0]
haml_time = File.stat(haml_file).mtime

html_file = CACHE_DIR_NAME + '/' + haml_file.sub(/aml$/,'tml')
if File.exists?(html_file)
  html_time = File.stat(html_file).mtime

  if html_time > haml_time
    output = File.read(html_file)
  end
end

if output.nil?
  require 'rubygems'
  require 'haml'
  template = File.read(haml_file)
  haml_engine = Haml::Engine.new(template)
  output = haml_engine.to_html()

  # cache the output
  Dir.mkdir(CACHE_DIR_NAME) unless File.directory?(CACHE_DIR_NAME)
  html_file_io = File.open(html_file,"w")
  html_file_io.print(output)
  File.utime(Time.now, haml_time, html_file)
end

# unbuffer output
$stdout.sync = true

require 'cgi'
ENV['SERVER_SOFTWARE'] ||= 'not set'
cgi = CGI.new('html3')
print cgi.header(
        'type'     => 'text/html',
        'charset'  => 'UTF-8',
        'length'   => output.length,
        'server'   => ENV['SERVER_SOFTWARE'],
        'expires'  => Time.now + 10*3600*24, # 10 days
        'Pragma'   => 'no-cache',
        'Last-Modified' => haml_time,
        'Cache-Control' => 'no-cache'
)
print output

And as Mike suggested, adding a couple lines to your Apache configuration makes all the difference:

  AddType text/haml .haml
  AddHandler haml-file .haml
  Action haml-file /dev/bin/haml_cache_cgi.rb
  Action text/haml /dev/bin/haml_cache_cgi.rb