Crack both eggs into a mixing bowl.
Whisk the eggs until completely combined.
Season with salt and pepper. If you're adding cheese or other fillings, make sure they are prepped and nearby.
Place the skillet over medium-high heat and melt the butter. Tilt the skillet as the butter melts to evenly coat the bottom. When the butter stops sizzling, the pan is heated and ready.
Pour the whisked eggs into the skillet. Immediately tilt the pan so the eggs coat the entire bottom. The eggs should sizzle on contact; if not, continue cooking, but remember to heat the pan a little longer next time.
Use a spatula to gently drag and push the cooked eggs from the edges toward the center of the pan, making space for the uncooked eggs and forming waves in the omelette.
Tilt the skillet so that the uncooked eggs flow into the open spaces.
The omelette will finish cooking in 1 to 2 minutes. When done, the bottom will be set and the edges will look crisp. The top of the omelette should still look fairly wet and uncooked, but there will no longer be any loose, easily-flowing liquid egg — the omelette will continue cooking off the heat, so finish when you think the top still seems a bit underdone.
If using, sprinkle the cheese and fillings down the center of the omelette.
Fold the bottom third of the omelette over the center.
Then fold the top third down. Alternatively, fold the omelette in half.
A well-made omelette is a thing of magnificence. It's soft and custard-like, golden-yellow, and best eaten while still piping hot from the skillet. An omelette makes a fantastic breakfast seasoned with just salt and pepper, but it's also a mighty fine delivery vehicle for anything from diced ham to sautéed mushrooms, eaten any time of day.