Combine the eggs, milk, salt, and pepper in a medium bowl and mix very well with a fork or a whisk. Set a plate by the stove. Heat a small (about 6 inches) seasoned omelette pan or non-stick skillet over medium-high heat.
When the pan is warm, add the butter (it should sizzle gently). Swirl the pan to distribute the butter as it melts. When the butter stops sizzling and the foam subsides add the eggs.
Pause to let the eggs heat slightly and then stir vigorously, with a heatproof spatula, making sure you include the sides of the egg mixture occasionally so the omelette cooks evenly.
Once the eggs are just set, bang the pan gently on the burner to release the omelet from the pan.
Check to see that it is not sticking to the sides or bottom of the pan, if so release the omelet with a heat proof spatula. Hold the pan at a 45-degree angle to the stove and carefully fold the omelette like a business letter.
Cook just until the desired degree of doneness lifting the pan or reducing the heat to prevent browning. (A classic omelet doesn't have any browning on it.) Transfer to a warm plate and serve.