Assemble the sandwiches by placing a slice of cheese and 2 slices of ham on a piece of bread and another slice of bread on top. Cut the sandwiches into quarters or halves and place cut side down in the baking dish.
Whisk together the egg, milk, and a generous pinch of salt and pepper. Pour over the sandwiches in the baking dish.
Let chill for at least 30 minutes or overnight.
Heat the oven to 350 degrees Fahrenheit. Transfer the dish to the oven and bake for 30-40 minutes or until the egg mixture is set and the sandwiches are golden.
Serve hot topped with powdered sugar and with jam to dip or dollop!
Notes
The nutrition information is calculated without the jam and powdered sugar for topping.