Crack the eggs into a bowl, add a pinch of salt and pepper, and whisk vigorously until well combined. The more you whisk, the airier and fluffier your omelette will be.
Place a non-stick skillet over medium heat. Add the butter and let it melt, ensuring it coats the bottom of the pan evenly.
Pour the whisked eggs into the pan, ensuring they spread evenly. Allow the edges to set slightly while gently lifting them with a spatula to let the uncooked eggs flow underneath.
Sprinkle the grated cheese evenly over one half of the omelette. Let it melt slightly.
Once the edges are set, use the spatula to fold the omelette in half, covering the cheese. Let it cook for an additional 1-2 minutes until the cheese is fully melted and the eggs are cooked to your desired consistency.
Slide the omelette onto a plate, garnish with fresh chives or herbs if desired, and serve immediately.
