package MyHandler;

use strict;
use warnings 'all';
use Apache2::RequestRec;
use Apache2::RequestUtil;

# Declare it here:
my $persistent_thing;

sub handler : method {
  my ($class, $r) = @_;

  # The first time this is executed in a child process, it will be created.
  # After that, you will just reuse the same one:
  $persistent_thing ||= make_the_thing();
}

1;