It becomes clear as what's going on, once we add some print outs at certain critical point (also see comments):

use Data::Dumper;

use strict;

sub prefix_later {
   my ($just_once,$and_later) = @_; #passed by calling part, see below
   my $ct=0;
   return sub {
      my (@args) = shift(); #this is just a trick ;-)
      print Dumper(\@args);
      print "ct = $ct\n"; #will not be reset to zero, becasue of closu
+re
      ((!$ct++) ? #only true for the first time
          sub {
             print "sub1\n";
             $just_once->(@args); #hi mom
          } : 
          sub { 
             print "sub2\n";    
             $and_later->(@args); #this was unneccessary:
             $just_once->(@args); #hi mom
          }
      )->();
   }
}

my $hi_mom = prefix_later( 
   sub { print "hi mom\n"; },#this is just once
   sub { print "this was unneccessary:\n"; } #this is and later
);

$hi_mom->() for (1..3);
[download]

Outputs:

#first round
$VAR1 = [
          undef
        ];
ct = 0
sub1
hi mom
#second round
$VAR1 = [
          undef
        ];
ct = 1
sub2
this was unneccessary:
hi mom
#third round
$VAR1 = [
          undef
        ];
ct = 2
sub2
this was unneccessary:
hi mom
[download]