For method 1: Melt butter in your pan, crack the egg into the pan, season with salt and pepper, top with cheese and cover and cook. Once cooked, serve. This should take 2 minutes approx on a low heat.
For method 2: Add grated cheddar on a non stick pan on a low heat. Let the cheese melt and then crack the egg on top. Season the egg with salt and pepper. Once the cheese has melted and crisped up and the egg cooked through, remove and serve.
For method 3: Gently beat the egg in a bowl, just enough to break the yolk but not beat it like you do for an omelet. Add some cheese to that and then fry in a pan. Serve.