In a skillet over low heat saute all the salmon slivers and parsley needed per omelette in butter until they are all warm and well coated. Remove and set aside.
Mix the eggs for one omelette in a separate small bowl with a teaspoon of water and salt and pepper. Stir briefly to break the yolks.
In an omelette pan over high heat melt 2 tablespoons of butter. As the foam subsides pour in the egg mixture, and shake the pan to even out the cooking of the eggs. Allow the eggs to cook for a few seconds, and then quickly add a portion of the smoked salmon mixture, spread in a line across the lower third of the eggs.
With a strong upward and backward hand motion repeatedly roll the omelette's near edge over the filling, using a spatula to help with the rolling if necessary. When the roll is complete allow the omelette to cook for a minute longer until the uncooked edges begin to curl slightly. Turn the omelette onto a serving plate and proceed for each additional omelette.