Place the smoked haddock skin side down in a pan and pour enough milk just to cover them. Remove the fish, bring the milk to a boil, then put the smoked haddock back in, reduce the heat, and simmer over low heat for 4 minutes.
Remove the smoked haddock from the milk and allow to cool while preparing the rest of the Cullen Skink ingredients. Strain the milk into a jug and set aside.
In another pot, add the butter and onions or leeks, and sauté for a few minutes until the onions are transparent, but not brown. Next, add the milk from the smoked haddock along with the rest of the original milk, the diced potatoes, and salt. Simmer gently until the potatoes are ready.
Meanwhile, prepare the smoked haddock. When the fish is cool enough to handle, pull the skin off (it comes off very easily).
Flake the fish into relatively large pieces.
When the potatoes are cooked, remove about one quarter to one half of the chowder (depending on how thick you like it). Pour into a container to puree (I use an immersion blender), then return to the pot.
Add the flaked fish, taste, and adjust the seasoning. Add some pepper, if desired. Cook for about two minutes to heat, but don't boil. Sprinkle of chopped parsley, and some hearty bread.