In a small frying pan, melt 1 ounce [2 tablespoons] of the butter over moderate heat.
When the foam subsides, add the smoked haddock and 2 tablespoons of cream, stirring well to mix.
When the cream is hot, remove the pan from the heat and set aside to cool.
In a large mixing bowl, beat the egg yolks with half of the cheese and the salt, pepper and parsley.
Add the fish mixture.
In another large mixing bowl, beat the egg whites with a wire whisk or rotary beater until they form stiff peaks.
With a metal spoon, fold the egg whites into the haddock mixture.
Preheat the grill [broiler] to high.
In a large omelet pan, melt the remaining butter over moderate heat.
When the foam subsides, pour in the egg mixture.
Leave it for 2 minutes or until the bottom sets and becomes brown.
Sprinkle over the remaining cheese and pour over the remaining cream.
Remove the pan from the heat and place it under the grill [broiler].
Grill [broil] for 30 seconds.
Remove the pan from the grill [broiler] and transfer the omelet to a warmed serving dish.
Cut into two or three and serve at once.