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Bring 400ml milk to a simmer along with 3 crushed cloves of garlic and sprig of thyme. Add the fish and cook for around 3 minutes or until the haddock starts to flake. Be careful not to overcook as it will become dry. Drain off the fish reserving the milk and flake up the fish into big pieces.
For the sauce: With the cooking milk from the fish, make a white sauce with 200ml of the milk, 20g butter, and 20g plain flour. Enhance the flavor with half a teaspoon of Dijon mustard, salt, pepper, and a few scrapes of nutmeg. Cool the sauce slightly and add the haddock flakes. Stir lightly being careful not to break up the fish too much. If the sauce is too thick, add a little more of the milk.
For the omelette: To cook the omelette, break 3 large eggs into a well buttered skillet pan. Season and stir, then let the egg cook out to form the omelette base. Remove from the heat and sprinkle on grated cheddar cheese and gruyere cheese. Add the haddock sauce mix to evenly cover the omelette. Sprinkle with a little more cheese and then place under a hot grill until lightly golden and bubbling. Finish with some chopped chives and parsley and serve from straight from the pan.