1. In a mixing bowl, whisk together the eggs and milk.
2. Assemble the sandwiches by layering ham, turkey, and cheese between two slices of bread.
3. Dip each sandwich in the egg mixture, making sure to coat both sides well.
4. Heat butter in a skillet over medium heat. Cook the sandwiches until golden brown on both sides and the cheese is melted, about 3-4 minutes per side.
5. Remove from skillet and dust with powdered sugar. Serve with jam if desired.
Notes:
For a twist, try using different cheeses or adding a slice of tomato.