Using a fork, beat the eggs, salt and pepper in a bowl until thoroughly mixed.
Heat the butter in an 8-inch, nonstick skillet until hot and the foaming has subsided. Pour the egg mixture into the center of the pan and cook over medium heat, allowing the eggs to set and curl at the edges. Then, with the tines of your fork, stir the eggs so the runny part fills the areas between the set curds. When most of the eggs are set but still slightly liquid inside, the omelet is ready.
Fold the omelet in half. You will notice that the outside will have a nice brown color. Invert onto a plate and serve immediately.