#!/usr/bin/env perl

use 5.012;
use warnings;
use strict;

$_ = do { local $/; <DATA> };
print "Match: $_" for /^\*+$ (.+?) ^\*+$/smxg;

__DATA__
Here's a text file

**********************************
You want the stuff in between the
asterisks, which is this sentence.
**********************************

**********************************
You probably want this too
**********************************

But not this

**********************************
Or this either