You can't, unless you create a reverse lookup as dragonchild suggests. Consider:

use strict;
use warnings;
use Data::Dump::Streamer;

my %hash = (
    doubleCheeseBurger => 'burger',
    cheeseBurger => 'burger',
    cheeseSandwich => 'sandwich',
    tomatoSandwich => 'sandwich',
    );
my %rHash;

push @{$rHash{$hash{$_}}}, $_ for keys %hash;

Dump (\%hash, \%rHash);
[download]

Prints:

$HASH1 = {
           cheeseBurger       => 'burger',
           cheeseSandwich     => 'sandwich',
           doubleCheeseBurger => 'burger',
           tomatoSandwich     => 'sandwich'
         };
$HASH2 = {
           burger   => [
                         'cheeseBurger',
                         'doubleCheeseBurger'
                       ],
           sandwich => [
                         'cheeseSandwich',
                         'tomatoSandwich'
                       ]
         };
[download]

Note that the reverse lookup hash has a list of entries for each key because of the many to one mappings in the original hash.