From the "Code References" section of the Storable documentation (with added emphasis):
Since Storable version 2.05, CODE references may be serialized with the help of B::Deparse. To enable this feature, set $Storable::Deparse to a true value. To enable deserialization, $Storable::Eval should be set to a true value. Be aware that deserialization is done through eval, which is dangerous if the Storable file contains malicious data.
In the demo below, a child process creates the hash of anonymous subs. Then the parent—in an entirely separate process and address space, so it can't see %dispatch—reads the output from freeze in the same way that you might from a file on disk.
#! /usr/bin/perl
use warnings;
use strict;
use Storable qw/ freeze thaw /;
my $pid = open my $fh, "-|";
die "$0: fork: $!" unless defined $pid;
if ($pid == 0) {
  # child process
  my %dispatch = (
    foo => sub { print "Yo!\n" },
    bar => sub { print "Hi!\n" },
    baz => sub { print "Holla!\n" },
  );
  local $Storable::Deparse = 1 || $Storable::Deparse;
  binmode STDOUT, ":bytes";
  print freeze \%dispatch;
  exit 0;
}
else {
  # parent process
  local $/;
  binmode $fh, ":bytes";
  my $frozen = <$fh>;
  local $Storable::Eval = 1 || $Storable::Eval;
  my $d = thaw $frozen;
  $d->{$_}() for keys %$d;
}
Output:
Hi!
Holla!
Yo!