Ah, that worked!

#!/usr/bin/perl -w

use strict;
use IO::Socket::SSL;

my $port = 12345;

my $server = IO::Socket::SSL->new(
    LocalAddr => '127.0.0.1',
    LocalPort => $port,
    Listen => 10,
    Reuse => 1,
    SSL_cert_file => 'cert.pem',
    SSL_key_file => 'key.pem',
) or die "failed to listen: $!";

my $client = $server->accept;
*STDOUT = $client;
print "The client should see this STDOUT message.\n";
print $client "The client should see this SOCKET message.\n";
close($client);
[download]

$ nc --ssl localhost 12345
The client should see this STDOUT message.
The client should see this SOCKET message.
[download]