Combine the eggs, milk, salt, and pepper in a medium bowl and mix very well with a fork or a whisk.

Set a dinner plate by the stove.

Heat a seasoned omelet pan or non-stick skillet over medium-high heat. When the pan is warm, add the butter. Swirl the pan so the butter gets all around.

When the butter stops sizzling and the foam goes away add the eggs. Let the eggs heat up (10 seconds).

Stir vigorously, with a heatproof spatula. When stirring, include the sides of the egg mixture so the omelet cooks evenly.

Once the eggs are set (the bottom starts to become solid and the edges start to dry a bit), thump the pan gently on the burner to release the omelet from the pan. Be sure that nothing is sticking to the sides or bottom of the pan, if so use a heat proof spatula.

Hold the pan at a 45-degree angle to the stove and carefully fold the omelet like a business letter. Shake the pan to create thin layers of egg. Fold omelet again and again forming thin layers all rolled up. Cook until just before the desired doneness lifting the pan or reducing the heat to prevent browning. (A classic French omelet is not brown like the American version.)

Transfer omelet to the warm plate and serve.