Dice the smoked haddock.

Steam the diced haddock and put it to one side, keeping it warm over the
cooking liquid.

Beat and season two eggs. Heat the oil, add the butter and pour the eggs
into the pan. While the omelette is still under done, put a quarter of the
haddock on top.

Turn the omelette onto a plate so that the haddock is underneath. Pour the
cooking liquid into the white sauce and make sure it is hot. Spoon sauce on
top of the omelette.

Sprinkle with grated cheese and breadcrumbs. Colour under the grill until
hot.