Whisk the eggs together in a bowl with the milk, a pinch of salt, and pepper if desired until light and frothy.

Layer two slices of bread with a slice of cheese on each. Add ham and turkey to one, top with another slice of cheese, then cap it off with the second slice of bread.

Dip the sandwich into the egg mixture, ensuring it is well-coated.

In a non-stick skillet, melt a tablespoon of butter over medium heat.

Place the soaked sandwich in the skillet and cook until golden brown, about 3–4 minutes on each side. Flip carefully to keep the melted cheese intact.

Remove from the skillet and let rest for a minute, then dust with powdered sugar if desired and slice in half.