In a bowl, beat the eggs with a pinch of salt and pepper until smooth.
Heat butter in a nonstick skillet over medium heat until melted. Pour in the eggs, tilting the pan to spread them evenly.
As the edges start to set, gently lift them with a spatula and tilt the pan to allow the uncooked eggs to flow underneath.
Sprinkle cheese and add fillings on one half of the omelette. Once the eggs are set but still slightly runny on top, fold the omelette in half over the fillings. Cook for another minute, then slide onto a plate.
Serve warm, topped with chopped herbs and other preferred toppings.