01 -
Whisk together eggs, kosher salt, and white pepper in a bowl until well combined.
02 -
Melt 2 tablespoons of unsalted butter in a large skillet set over medium heat.
03 -
Spread the remaining 1 tablespoon of butter on one side of each bread slice and set aside.
04 -
Pour the egg mixture into the skillet, tilting the pan to distribute it evenly. Position both bread slices, buttered side up and edges touching, directly on top of the eggs.
05 -
Allow eggs to cook undisturbed for 5 to 7 minutes, or until the eggs are set and no longer runny.
06 -
Carefully invert the eggs with the bread attached, ensuring the eggs are fully set to assist in flipping.
07 -
Place cheddar cheese on one bread slice, then layer with the ham. Fold any overhanging egg onto the ham.
08 -
Fold the second bread slice over the filling to enclose. Flip the sandwich and cook an additional 2 to 3 minutes, or until the cheese melts and the outside is golden brown. Serve immediately.