Pat the Smoked Haddock dry and set aside; this will be gently poached later.
Thinly slice the Onion and dice the Floury Potatoes into even 1–2 cm cubes.
Melt the Unsalted Butter in a large saucepan over medium heat and sweat the sliced Onion until soft and translucent, about 6–8 minutes — do not brown.
Pour in the Whole Milk and enough Water to just cover the potatoes (about a 2:1 milk-to-water ratio overall), then add the Bay Leaf and a generous grind of Black Pepper.
Add the diced Floury Potatoes to the pot, bring the liquid to a gentle simmer, then reduce heat and cook until the potatoes are tender, about 12–15 minutes.
Gently slide the Smoked Haddock into the simmering liquid during the last 6–8 minutes of the potatoes' cooking time; poach until the fish is opaque and flakes easily.
Remove the poached Smoked Haddock to a plate, discard the Bay Leaf, then use a slotted spoon to lift some potatoes into a bowl and mash lightly — return them to the soup to help thicken the broth.
Flake the cooled Smoked Haddock, removing any skin and bones, and stir the flakes back into the pot. Warm gently for 2–3 minutes to combine flavors, but avoid boiling.
Season to taste with Salt and more Black Pepper if needed. Finish with a generous sprinkle of chopped Parsley and an extra knob of Unsalted Butter if you like for added silkiness.
Ladle into bowls and serve hot with crusty bread for soaking up the smoky, creamy broth.
