Crack the eggs into a mixing bowl and whisk them until well mixed.
Season the beaten eggs with salt and pepper, then stir in the grated cheese until evenly distributed.
Heat a non-stick skillet over medium heat and add the butter.
Once the butter is melted and hot, pour the egg and cheese mixture into the skillet.
As the omelette begins to set, use a silver fork to gently draw the thickening portions from the bottom of the pan, allowing the liquid egg mixture to cover the pan.
Repeat this process until the omelette is mostly set but still slightly runny on top.
Once the omelette is cooked to your liking, carefully fold it in half using a spatula.
Transfer the folded omelette onto a heated plate.
Garnish with chopped parsley or cress.
Serve the Classic Cheese Omelette immediately while hot.