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In a medium bowl combine eggs, salt, and pepper.
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In a large skillet, melt 2 tablespoons of butter over medium heat.
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Use the remaining tablespoon of butter to butter one side of each of the two slices of bread. Set aside.
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Once the butter has melted in the skillet, add eggs. Swirl the pan to get the eggs to reach the edges.
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Add both slices of bread, butter side up and touching bottom edge to bottom edge, on top of the eggs.
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Cook undisturbed until eggs are no longer runny (5-7 minutes).
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Flip over the cooked eggs with both slices of bread. (If your eggs are cooked, it should be easy to flip.)
- Top one slice of bread with cheese and then ham. Fold the excess egg on top of the ham.
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Fold the other slice of bread over top to make the sandwich.
- Flip and cook 2-3 more minutes, or until the cheese is melted and the sandwich is browned and heated through. Serve warm.