In a shallow dish whisk together egg and milk. Season with kosher salt and pepper and set aside.
Lay out 2 slices of bread and top in this order - 1 tablespoon of cranberry sauce, 1 slice of Swiss cheese, an equal amount of leftover turkey, and 1 handful of arugula.
Cover the other slices of bread with 1 tablespoon each of cranberry sauce and top the sandwich.
In a large skillet or griddle set over medium heat add 2 tablespoons butter. Let the butter melt and get hot.
Once the butter is hot dip the sandwich (both sides) into the egg mixture and add the sandwiches to the prepared skillet.
Cook until the bottom is golden brown and flip. If the skillet needs more butter add a little more butter to the skillet.
When you remove the sandwich from the skillet the cheese should be melted (and the inside of the sandwich will be hot) and the outside will be golden brown.
Serve hot with extra cranberry sauce and sprinkled with powdered sugar.