Heat a 9-inch non-stick or cast iron skillet over medium-high heat. Add the butter and swirl it around to coat. When the butter has turned foamy and the little bubbles are starting to disappear, pour the eggs in the skillet. Tilt the pan to coat the eggs evenly over the surface of it. Use a spatula to lift a corner of the omelet. If the eggs have begun to set, sprinkle evenly with cheese and any vegetables you may be using. Using the spatula and tilting the pan away from you, fold the omelet in half. Continue cooking for 1 minute. Slide the omelet off the pan onto a plate and sprinkle with salt and pepper. Enjoy hot.