Mix the milk with 300 ml water, pour it into a large shallow pan and bring to the boil. Add the bay leaves, onion and lemon slices, peppercorns and smoked haddock. Simmer for 3-4 minutes until the fish is just cooked.
Lift the fish out of the pan and leave until cool enough to handle. Now break it into flakes, discarding any skin and bones.
Preheat the grill to high.Whisk the eggs together with some seasoning. Heat a 23-25 cm frying pan over a medium flame then add the butter and swirl it round to coat the base and sides of the pan.
Pour in the eggs and, as they start to set, drag the back of a fork over the base of the pan, lifting up little folds of egg to allow the uncooked egg to run underneath.
When the omelette is set underneath but still very moist on top, sprinkle over the flaked smoked haddock. Pour the cream on top, sprinkle with the parmesan cheese and put the omelette under the hot grill until lightly golden brown.