Start by poaching the smoked haddock fillets in a pan of simmering water for about 8-10 minutes until cooked. Once done, remove the haddock from the water and set aside to cool. Once cooled, flake the haddock into small pieces, discarding any skin or bones.

In a large pot, melt the butter over medium heat. Add the chopped onion and sliced leeks, and cook until they become soft and translucent, about 5 minutes.

Add the diced potatoes to the pot and stir to coat them with the buttery mixture. Cook for another 2-3 minutes.

Pour in the fish or vegetable stock and bring the mixture to a simmer. Let it cook for about 10-15 minutes or until the potatoes are tender.

Add the flaked smoked haddock to the pot, followed by the milk and cream. Stir gently to combine all the ingredients and let the soup simmer for another 5 minutes.

Season with salt and pepper to taste. Remember, the smoked haddock is already naturally salty, so be careful not to over-season.

Once the soup is heated through, remove from the heat and let it cool slightly. You can use a handheld blender or a regular blender (in batches) to blend the soup until smooth, or you can leave it chunky if you prefer a more rustic texture.

Return the soup to low heat, allowing it to warm up before serving. Make sure it doesn't boil.

Ladle the Cullen skink into bowls, garnish with chopped fresh parsley, and serve hot with crusty bread or buttered rolls.