In a bowl, whisk together 4 eggs, 1/4 cup of milk, salt, and black pepper to taste until well combined.
Heat 1 tablespoon of oil or butter in a non-stick pan over medium heat.
Pour the egg mixture into the pan and let it cook for 2-3 minutes until the edges start to set.
Sprinkle 1/2 cup of grated cheese (such as cheddar or mozzarella) evenly over the omelette.
Gently fold the omelette in half using a spatula, covering the cheese.
Cook for another 2-3 minutes, or until the cheese has melted and the omelette is cooked through.
Carefully slide the cheese omelette onto a plate and serve hot with toast or a side salad.