In a large mixing bowl, crack the eggs and whisk them until well combined.
Add the shredded cheese, salt, and pepper to the eggs, and mix everything together.
If you're using vegetables, you can sauté them in a separate pan until they're slightly softened.
Heat a non-stick skillet over medium heat and add 1/2 tablespoon of butter.
Once the butter is melted and the pan is hot, pour a quarter of the egg mixture into the skillet.
Let the eggs cook for a minute or two until the edges start to set.
Using a spatula, gently lift the edges of the omelette and tilt the pan to let the uncooked eggs flow to the edges.
When the eggs are mostly set but still slightly runny on top, sprinkle your sautéed vegetables (if using) on one half of the omelette.
Carefully fold the other half of the omelette over the vegetables to create a half-moon shape.
Cook for another minute or two until the cheese is melted and the eggs are cooked through.
Slide the omelette onto a plate and repeat the process with the remaining egg mixture and butter.
Enjoy!