Place the smoked haddock in a saucepan and pour in the milk. Heat gently for about 5 minutes. This step softens the fish and infuses the milk with smoky flavor.

Take the fish out of the milk and place it on a plate. Use a fork to break the fish into large flakes. Save the milk because it will be used later in the soup.

In a large soup pot, melt the butter over medium heat. Add the chopped onion and cook slowly for about 5 minutes. The onion should become soft and slightly sweet.

Add diced potatoes to the pot with the onions. Stir gently so the potatoes mix well with the butter and onion. This step starts building the base flavor.

Add the fish stock or water to the pot. Bring the mixture to a gentle boil. Then reduce the heat and simmer for about 10 minutes until the potatoes become tender.

Pour the reserved milk from the fish cooking into the pot. Stir gently and allow the soup to warm slowly. The milk adds creamy texture and smoky flavor.

Add the flaked smoked haddock to the soup. Stir carefully so the fish stays in chunky pieces. Cook for another 5 minutes to blend the flavors.

Add black pepper and salt to taste. Taste the soup and adjust seasoning if needed. The smoked fish already adds natural saltiness.

Stir in the heavy cream if using. Sprinkle chopped parsley on top. The cream makes the soup richer while parsley adds freshness.

Ladle the soup into bowls and serve warm. Cullen Skink tastes best when fresh and hot.