#!/usr/bin/perl
use strict;
use warnings;

my $string =<<"HERE";
I have some <brackets in <nested brackets> > 
and
<another group <nested once <nested twice> > >
and that's it.
HERE

my @groups = $string =~ m/(<(?:[^<>]++|(?1))*>)/g;

$" = "\n\t";
print "Found:\n\t@groups\n";