In a small mixing bowl, break both eggs, add cold water, salt and pepper and using a fork or a whisk, mix until well blended.
Preheat an 8 or 10 inch frying pan on medium-high heat. It is preferable to use a non-stick frying pan or skillet.
Add butter and let it melt.
Rotate pan and let the butter coat the edges.
Pour the egg mixture into the center of the pan and immediately start to rotate the pan in a circular motion, keeping the pan on the element at all times.
During rotating, take a spatula and loosen the egg on the sides of the pan if nececessary and continue to rotate the pan until the eggs are cooked. You may need to loosen the sides a couple of times during cooking; takes about 2 minutes. The omelette should be loose and rotate in the pan. Do not overcook the omelette as it will get rubbery.
Once the omelette is cooked, take the spatula and turn 1/3 of the omelette over towards the center of the pan. Slide the omelette onto a platter so that it folds again.
You may wish to use your choice of filling. Just before you fold the last 1/3 over, add some filling and then fold the omelette over.
Do not let the omelette brown. It should be thin and soft.