It all turned out to be simpler than I thought.
Just remember: LEAVE A BLANK LINE AFTER "Content Type: " setting
Simple as that. So, here's the working code for sending text along with an attached file:

my $smtp = Net::SMTP->new($host);

$smtp->mail($myemail);         
$smtp->to(@emails);

# Start the mail
$smtp->data();       
                   
# Send the header. There needs to be a newline at the end of each line
$smtp->datasend("To: Myself\n");
$smtp->datasend("From: Me\n");
$smtp->datasend("Reply-To: oakulov\@rim.com\n");
$smtp->datasend("Subject: Test email\n");
$smtp->datasend("MIME-Version: 1.0\n");
$smtp->datasend("Content-Type: multipart/mixed; boundary= \"*BCKTR*\"\
+n\n");
 
# Send the body.
$smtp->datasend("--*BCKTR*\n");
$smtp->datasend("Content-Type: text/plain\n\n");  # this is a formatti
+ng command, so leave an extra line between it and the text
$smtp->datasend("This is a test email\n");

# Send attachemnt
my $buffer = "";
my $file = "Test.txt";
open (MAIL, "<$file") or die "ERROR: Could not open email file";
  while (<MAIL>) {$buffer .= $_}
close (MAIL);

$smtp->datasend("--*BCKTR*\n");
$smtp->datasend("Content-Type: text/plain; name= \"$file\" \n");
$smtp->datasend("Content-Disposition: attachment; filename= \"$file\"\
+n\n");
$smtp->datasend("$buffer\n\n");

# Send the END section break
$smtp->datasend("--*BCKTR*--\n\n");  

# Finish sending the mail
$smtp->dataend();
# Close the SMTP connection
$smtp->quit;
[download]