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. Cooke for two or three minutes longer to get everything heated through.
In a small bowl whisk together the eggs, water, and Worcestershire sauce until a bit frothy. Season with salt and pepper and pour into the skillet. Cook until edges are just set, occasionally pulling in from the edges with a small spatula. Swirl pan and repeat once or twice. Cook until set. 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 cheese melt.
Serve with ketchup or 1000 dressing and other cheeseburger fixings if desired.
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