You are thinking about hashes of hashes in the incorrect way. Hash elements and array elements must be scalars, so when dealing with a complex structure you are really storing hash references (pointers to hashes) in the hash. So rather than the nested access approach you have, reading a deep entry should look like

$servers{$server}{$process}

which is short hand for

$servers{$server}->{$process}

This means, for iterating through a hash of hashes using keys, your code should look like:

foreach $server (keys %servers) #returns individual servers
{
        print "$server\n";
        foreach $process (keys %{$servers{$server}}) #returns individu
+al processes on a server
        {
                print "$process\n";
                foreach $processPart (keys %{$servers{$server}{$proces
+s}}) # returns part of a process
                {
                        print "$processPart\n";
                }       
        }       
}
[download]

For some more details on these types of structures, you should probably read perllol.