Put the ling in a pan of fresh water with the onions and bay leaves, bring to the boil, then turn down to a simmer for 14 minutes.
Meanwhile place your potatoes in unsalted water, bring to the boil, and cook until soft enough to mash, and hardboil your eggs so that the yolks are soft and slightly giving.
Drain the fish, discard the onions and bay leaves, and let it cool until you can handle it, then pull the flesh away from the skin and bones—be warned, this is a very sticky exercise.
You should now have warm salt fish and drained hot potatoes. Heat the milk and butter and add half to the potatoes and mash. Add the fish flesh, and keep mashing—you should start to have a pan of hairy mashed potatoes. If they are too stiff add a little more milk and butter. Check for seasoning; it will certainly need black pepper but depending on the fish you may or may not need salt.
Serve a hairy mound with a hardboiled egg, in its shell.