Break the eggs into a stainless steel bowl and beat with a whisk to a smooth consistency. Salt and pepper can be added now, immediately before cooking to allow full incorporation into the eggs.
Heat the pan over medium to low heat. Add the butter and allow to heat to a bubbly state without burning or browning. Add the beaten eggs to the pan and immediately begin to stir the eggs in a circular fashion so they do not stick to the bottom at the same time that you shake the pan across the burners. Keep the pan moving, stirring with your spatula, so that as the eggs begin to cook and coagulate, you pull cooked egg from the outer edge of the pan over raw egg in the center.
When the eggs are half cooked, cease stirring and shaking the pan, and now roll the raw and runny egg outward by twisting your wrist. The uncooked egg will now cook on the bottom and sides of the pan. The entire cooking process will take at most 2 minutes and experience will be the best teacher to master the classic omelette. The omelette should not brown but should stay a beautiful egg golden.
.Give the pan 1 or 2 good firm raps on the burner and, holding the handle in one hand in an underhanded grip, tilt the handle upward and begin to roll the edge of the omelette furthest away from the serving dish towards the plate. Roll this edge of the omelette one third towards the center, begin to slide the front of the omelette out onto the plate so the leading edge becomes the seam of the omelette and is flatly on the bottom. This will from the perfect oval shaped omelette.
To make filled omelettes, add cooked vegetables, cheese or meats to the center of the omelette just before you begin to roll the omelette for the finished plate. Always heat fillings separately and cut the meat and cheese thinly enough to be thoroughly heated by the heat from the omelette center.
Suggested fillings: Sauteed mushrooms and goat cheese, fresh herbs; thyme, chives, tarragon, parsley, sauteed spinach, cheddar cheese and jalapeno pepper, cooked bacon or country ham ratatouille