This is only briefly tested. The problem with only getting level 2 and not 1, is that you can't prune level 1, without pruning level 2. This script is only briefly tested, play with it. Instead of prune, use a simple return.

#!/usr/bin/perl
# linux only
use warnings;
use strict;
use File::Find;
use File::Spec;


my ($path, $depth)= ('.', 2);

my $abs_path = File::Spec->rel2abs($path); #in case you enter . for di
+r
my $m = ($abs_path) =~ tr!/!!;  #count slashes in top path

find (\&found,$abs_path);
exit;

sub found{
 my $n = ($File::Find::name) =~ tr!/!!; #count slashes in file
 print "$m $depth $n  ";

 return  unless $n == ($m + $depth );
 
   # do stuff here.
   #print "$_\n";                #name only

 print "$File::Find::name\n";  #name with full path
}
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