Heat a 10-inch nonstick skillet over medium heat; add butter. When your palm placed over the skillet feels very warm, the skillet is ready.
While the pan is heating, in a medium bowl whisk together eggs, and season with salt and pepper; incorporate a lot of air into eggs, so that the omelet will be light and fluffy.
Pour eggs into the hot skillet. Simultaneously, briefly whisk eggs and shake the skillet vigorously back and forth over the heat, until eggs begin to set. Stop whisking, and let cook until almost completely set, 1 to 1 1/2 minutes.
With the handle of the skillet facing you, sprinkle the left half of the omelet with grated cheese. Using a rubber spatula, carefully loosen eggs from the edges of the skillet, and then fold the right half of the omelet over filling, forming a half-moon shape. Lightly press down on the omelet with the spatula to seal it together.
Lift up the skillet with one hand and a serving plate with the other. Tilt the skillet, and let the curved edge of the omelet slip onto the plate. Quickly invert the skillet, folding the portion of the omelet that is left in the skillet over the curved edge already on the plate. Serve immediately.
It is important to heat the pan before adding the butter to prevent sticking.