Heat a small skillet over medium heat. Add the butter and swirl to coat pan. Add the onion and cook for 3 to 4 minutes.
Add the cheeseburger patty and break up into small pieces. Cook for two or three minutes longer to get everything heated through and onion is softened.
Remove the beef and onion from the pan and set aside.
In a small bowl whisk together the eggs, water, and Worcestershire sauce until a bit frothy.
Pour the egg mixture into the skillet. Cook until edges are just set, occasionally pulling in from the edges with a small spatula, sweeping in towards the center.
Swirl pan and repeat once or twice. Cook until the bottom is almost set but the top is still a bit wet. Add the burger and onion to the center of the omelet.
Get fancy and flip if you want things to possibly end badly (not saying that I'm speaking from experience or anything). Otherwise, fold over and sprinkle with cheese. Cover and let the cheese melt, about 1 minute longer.
Off heat, season with salt and pepper. Transfer the omelet to a serving plate.
Serve with ketchup or 1000 dressing and other cheeseburger fixings if desired.
This recipe uses one leftover cooked burger patty. If you dont have one, you can use cooked ground beef as well.