Slice each cinnamon bun in half, and place the slices on a work surface. To assemble a sandwich, place the toppings in this order: bottom of cinnamon bun, 1 slice Cheddar cheese, 1 slice of Brie cheese, apple slices, shredded ham, 1 slice of Brie cheese, 1 slice of Cheddar cheese, top of cinnamon bun. Repeat for 2nd sandwich, and gently press each sandwich together.