To make an omelet, combine the eggs with water, salt, and pepper according to the recipe. Stir with a whisk until blended. Heat an omelet pan or heavy skillet over medium heat. Add butter to the pan, tilting the pan until the butter has melted and coated the bottom of the pan. Pour the egg mixture into the pan. As the mixture starts to cook, gently lift the edges of the omelet with a spatula and tilt the pan so that the uncooked portions flow underneath. Keep doing this until the egg mixture is almost set. Sprinkle half of the omelet with chopped ham or cheese, or other desired fillings. Fold the omelet in half and cook until the cheese melts. Transfer the omelet to a serving plate.