sending a large file via http

[mifflin]

I have client that wants me to send him a file via http.
The potential problem here is this file may be rather large (megabytes).
The usual way that I send data through http is via the POST method like...

   my $headers = HTTP::Headers->new();
   $headers->header('Content-Type' => 'text/plain; charset=utf-8');
   $headers->header('Content-Length' => length($sendthis));
   my $request = HTTP::Request->new('POST', $url, $headers, $sendthis)
+;
   $request->protocol('HTTP/1.1');
   my $browser = LWP::UserAgent->new();
   my $response = $browser->request($request);
   my $gotthis = $response->content();

This works but can result it memory issues if the variable $sendthis is large.
Is there a better way to send large files via http?