Omelette Arnold Bennett

Name: Omelette Arnold Bennett
Ingredients: For the haddock:; 1 fillet of smoked haddock (Finnan, if possible) – undyed, skin and bones removed; 500ml milk; Sprig of fresh thyme, leaves picked; 2 cloves of garlic, crushed; For the hollandaise sauce:; 4 egg yolks; 2 tbsp white wine vinegar; 2 tbsp water; 1 tbsp English mustard; 250g butter, melted; For the béchamel sauce:; 250ml milk (retained from the haddock, above); 1 bay leaf; 2 cloves; 6 black peppercorns; 15g butter; 15g plain flour; Pinch of white pepper; 50g cheddar, grated; 50g Gruyère, grated; For the scrambled eggs:; 4 eggs