In a large saucepan, bring the milk up to the boil. Place the smoked haddock in the milk, and turn off the heat. Place a lid on the pan, and leave the haddock to gently poach in the milk for 8 to 10 minutes.
Remove the haddock from the pan, and cover with foil to keep warm. Remove all bones, and discard the bones and skin. Pass the poaching milk through a fine sieve into a jug.
In a saucepan, melt half the butter, and then add the flour. Mix to form a smooth paste. Gradually add half the poaching milk in batches, stirring all the time, to make a white sauce.
In a medium bowl, whisk the whole eggs with some salt and pepper. In a large nonstick frying pan, melt the remaining butter over low heat. Pour the whisked eggs into the pan, and cook slowly. When just cooked, remove the eggs from the heat, and cover with the Parmesan. Add the chives, and place flakes of smoked haddock over the top.
Preheat the grill to the broiler setting.
In a mixing bowl, mix together the egg yolks, creme fraiche and 6 tablespoons of the white sauce. Spoon this mix over the top of the omelette, and place under the broiler to make a glaze. (Alternatively, use a kitchen torch.)