In a small bowl, beat the egg and the half & half until well combined. Set aside. Spread one slice of bread with mayonnaise and the other slice with mustard. Top each slice of bread with 2 slices Swiss cheese. Place ham on one slice bread and assemble sandwich by topping it with the other slice. In a small skillet, melt butter over medium heat. When the butter begins to bubble, dip the sandwich quickly in the egg mixture, making sure the entire sandwich is coated Add sandwich to skillet and cook until golden brown on one side. Flip and cook the other side. Sprinkle with powdered sugar, if desired. Serve warm.