sort's second argument is a list. %H, as a list, would look like ('key2', 'value2', 'key1', 'value1', 'key3', 'value3'). That means that by_date would be provided not just with the values, but with the keys as well.

Here's a solution:

sub by_date {
   my ($monA, $monB, $dayA, $dayB, $yearA, $yearB);

   ($monA, $dayA, $yearA) = split(/\//, $a->[1]);  # <-- slight change
   ($monB, $dayB, $yearB) = split(/\//, $b->[1]);  # <-- slight change

   $yearA <=> $yearB
   or
   $monA <=> $monB
   or
   $dayA <=> $dayB
}

@H = map { [ $_, $H{$_} ] } keys(%H);
foreach $k (sort by_date @H)) {
   # $k->[0] is the key.
   # $k->[1] is the value.
   ...
}
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