Gently poach the haddock in the fish stock for 7–8 minutes or until just tender. Allow to cool then remove any skin and bones.
Flake the haddock, mix with the cheese and season to taste with salt and pepper. Put the eggs into a bowl and lightly beat with the water.
Melt the butter in an omelette pan and pour in the egg mixture. When the eggs begin to set, put the fish and cheese on top. While they are still liquid, pour over the cream then put the pan under a preheated hot grill for a few minutes until the top is golden brown. Do not fold the omelette but slide it on to a hot plate and serve immediately.