Crack the eggs into a bowl. Add a pinch of salt and pepper. Whisk vigorously until the yolks and whites are fully combined and slightly frothy.

Heat a non-stick skillet over medium-low heat. Add the butter and let it melt, swirling to coat the pan evenly.

Pour the whisked eggs into the skillet. Let them sit for a few seconds until the edges start to set.

Using a spatula, gently push the set edges toward the center, tilting the pan to let the uncooked eggs flow to the edges. Repeat until the eggs are mostly set but still slightly runny on top.

If adding fillings like cheese or ham, sprinkle them over one half of the omelette now.

Fold the omelette in half with the spatula. Let it cook for another 10-20 seconds, then slide it onto a plate. Garnish with chopped chives if desired.