Fold the slices of cheese in half and then in half again and wrap each one in a slice of turkey.
With a paring knife, make slice in the top of each slice of bread and cut about 3/4 of the way through the slice to make a pocket. Stuff one of the Swiss-turkey bundles inside each pocket.
Place a medium-size nonstick skillet over medium heat and melt the butter. Combine the beaten egg in a shallow bowl or dish with the milk. Add the stuffed bread to the egg mixture and coat both sides in the egg.
Place the egg-coated bread in the skillet and cook on both sides until golden brown. Serve with a little drizzle of maple syrup on the top or a small bowl of syrup alongside for dipping, if desired.