my $str =
  q{[S [NP This NP] [VP is [NP [PP to [NP the left NP] PP] NP] VP] . S]};

my $bracket;

$bracket = qr{
  (?:
    (?> [^][]* )
    |
    \[ (??{ $bracket }) \]
  )+
}x;


for (get_brackets($str, 1)) { print "<$_>\n" }
for (get_brackets($str, 2)) { print "<<$_>>\n" }


sub get_brackets {
  my ($str, $depth) = @_;
  my @hits = $str;
  @hits = map m{\[($bracket)\]}g, @hits
    for 1 .. $depth;
  return map "[$_]", @hits;  # put the []'s back in
}