Place smoked haddock in a pot with milk and water. Bring it to a gentle simmer. Cook for about 8 minutes until tender. Remove fish carefully and set aside. Keep the cooking liquid for later use.

In another pot, melt butter over medium heat. Add chopped onions and cook slowly until soft and light golden. Stir often to avoid burning. This step builds a sweet and soft flavor base.

Add diced potatoes into the pot with onions. Pour in the reserved milk mixture from the fish. Stir gently and let it simmer. Cook until potatoes are soft and easy to mash.

Take the cooked haddock and remove skin and bones carefully. Flake the fish into small pieces. Make sure the pieces are bite-sized and soft.

Add flaked fish into the pot with potatoes. Stir gently so the fish mixes well. Let it cook together for a few minutes. This helps flavors blend nicely.

Lightly mash some potatoes in the pot. This thickens the soup naturally. Do not mash all pieces. Keep some chunks for texture. Add salt and black pepper to taste.

Turn off heat and let the soup rest for a few minutes. Sprinkle fresh parsley on top before serving. Serve warm and enjoy the creamy texture.