Mix the milk with 300ml/10fl oz of water toghether, pour it into a large shallow pan and bring to the boil.
Add the bay leaves, onion slices and peppercorns and bring back to the boil.
Add the smoked haddock and simmer gently and poach for about 3-4 minutes, until the fish is cooked. Lift the fish out on to a plate and leave until cool, then break into flakes, discarding any skin and bones.
Pre-heat the grill to high.
Whisk the eggs together with some seasoning.
Heat a 23-25cm/9-10 inch non-stick frying pan over a medium heat, then add the butter and swirl it around 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 parmesan cheese and put the omelette under the hot grill until lightly golden brown.
Slide it on to a warmed plate and serve with a crisp green salad.
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