Poach the smoked haddock in milk for about 10 minutes, then drain and flake the flesh. Keep the fish warm.
Whisk the eggs, a seasoning of salt and pepper and the milk together. Use the milk from poaching the smoked haddock if you wish, it gives a lovely flavour to the mixture but go easy on the seasoning added.
Melt the butter in a frying pan and pour in the scrambled egg mixture. Cook over low heat, drawing a spoon across the pan to lift up the egg mixture as it sets. Add the flaked haddock. Draw the pan off the heat when the mixture is thickened but still moist. Serve on slices of buttered toast.