Heat a nonstick skillet over medium-high heat. Melt the butter in the pan, turning it slightly to spread it all around.
Meanwhile, whisk together the eggs, salt and pepper with a fork . Once the butter is melted and just about turning golden, pour the eggs into the hot pan.
Let them cook for about a minute, until a film of egg forms on the bottom. Then, tilt the pan at a shallow angle (Julia says 20 degrees) and vigorously jerk the pan, shaking the eggs free from the bottom and periodically lowering it down to spread the still liquid eggs around. Continue until the top is shiny and moist but no more egg moves around when you shake the pan.
Sprinkle the cheese all over the omelet. Let sit for a minute. Then, holding the pan at a more dramatic angle, grasp the handle firmly with two hands and vigorously shake until the omelet rolls over on itself.
Slide the omelet onto a plate and sprinkle with tomatoes. Serve immediately.