Simmer milk, haddock, bay leaf, and peppercorns in a pan for five minutes.
Remove the fish from the pan, cool slightly, and flake it into pieces while discarding the skin.
Strain the poaching milk into a clean container and beat the eggs in a separate bowl.
Melt 15g of butter in a frying pan over medium-hot heat and cook the eggs gently while stirring.
Place half the flaked fish on the omelette and roll it onto an ovenproof dish before adding the remaining fish.
Preheat the grill to a hot setting.
Melt 25g of butter in the pan, stir in the flour for two minutes, then whisk in the milk to form a sauce.
Season the sauce and pour it over the omelette.
Scatter cheese over the top and grill for 3-5 minutes until golden-brown.
Serve the dish immediately.