Poach the haddock and onion clouté in the milk for 3 to 4 minutes. Drain and flake the fish, keep the cooking liquor.

To make the sauce, melt the butter. When foaming add the flour and cook out for a minute. Whisk the poaching milk, then the cream and season. Stir in half of the cheese.

To make the omelette, whisk together the eggs and season. Heat a large non-stick frying pan and add the butter. When foaming, add the egg mix and turn the pan down to a medium heat, using a fork bring the edges of the eggs in, when starting to firm up. Dot with haddock and spoon over the sauce. Sprinkle over the remaining cheese and grill until golden and bubbling. Serve with dressed green salad.