Beat the eggs in a bowl, season with salt and pepper, and mix in the diced ham. Heat the butter in a skillet over medium heat.

Pour the egg mixture into the skillet, allowing it to set slightly at the edges. Sprinkle the grated cheese over one half of the omelette.

Once the omelette is mostly set, fold it in half to cover the cheese.

Continue cooking until the cheese is melted and the omelette is cooked to your liking.