It's easy to optimize a bit, although it's still 20% slower than Aristotle's version :-(

my %cache = ('-1' => qr/([^\(\)]+)\)+\Z/);

sub peel {
  my $str = shift;
  my $level = shift || 0;
  if (!exists $cache{$level}) {
    my $opening = '[^\(]+\(' x $level;
    my $closing = '\)' x $level;
    $cache{$level} = qr/\A$opening(.+?)$closing\Z/;
  }
  $str =~ $cache{$level};
  return $1;
}
[download]

             Rate   Fatvamp       gjb      bobn Aristotle
Fatvamp   21155/s        --      -14%      -17%      -28%
gjb       24631/s       16%        --       -3%      -16%
bobn      25523/s       21%        4%        --      -13%
Aristotle 29497/s       39%       20%       16%        --
[download]

Best regards, -gjb-