Assemble the sandwiches with two slices of bread, one slice of ham, one slice of turkey, and two slices of Swiss cheese.
In a shallow dish, whisk together eggs and milk.
Dip each sandwich in the egg mixture, coating both sides.
Melt butter in a large skillet over medium heat. Cook the sandwiches until golden brown on both sides and cheese is melted, about 3-4 minutes per side.
Dust with powdered sugar before serving.
Notes
For an extra touch, serve with a side of raspberry jam.