In a bowl, beat eggs with salt and pepper.
Heat butter in a skillet over medium heat. Add vegetables and cook until softened.
Pour beaten eggs into the skillet and cook until the edges start to set.
Sprinkle cheese over one half of the omelette. Fold the other half over the filling.
Cook for another minute until the cheese is melted and the eggs are cooked through.
Slide the omelette onto a plate and serve hot.