Preheat the oven to 190'C.
Break the three eggs into a bowl, add the salt and pepper and beat together. Set aside while you prepare the other elements of the recipe.
Grate the cheddar.
Place the butter in a large saucepan and allow to melt over a medium heat. Once melted, add the flour and mix well over the heat. Once the mixture begins to thicken, start slowly whisking in the milk. Keep whisking to prevent the sauce from burning as it thickens. Remove from the heat and then add the grated cheese. Mix well and then incorporate the egg yolk. Add the seasoning and set aside.
Cut the smoked haddock into 1cm dice and place in a saucepan with the milk. Bring to the boil and simmer for one minute - the smoked haddock will just begin to cook. Remove from the heat and strain.
Heat a medium sized non-stick frying pan. When hot, add the beaten egg mixture and mix well using a spatula. Flatten the mixture to make the omelette. Remove from the pan and sprinkle the smoked haddock over the top. Spoon the Mornay sauce over the top, ensuring that all of the haddock is covered. Transfer the pan to the oven and cook for 3 to 4 minutes to give a nice glaze to the omelette. Remove from the oven and serve immediately.
«There is no salt in the bechamel mixture as the smoked haddock tends to be salty. Extra salt can be added to the mixture if you prefer. »