On four of the bread slices layer ham, cheese, and apples. Spread the remaining four bread slices with cranberry sauce; place on sandwiches, cranberry sides down. Brush outsides of sandwiches with oil.
Preheat a covered indoor grill, panini press, grill pan, or large skillet. Place sandwiches, half at a time if necessary, in grill or panini press. Cover and cook about 6 minutes or until golden brown and cheese is melted. (If using a grill pan or skillet, place sandwiches on grill pan or skillet. Weight sandwiches down with a heavy skillet [add food cans for more weight] and cook for 2 minutes. Turn sandwiches over, weight down, and cook about 2 minutes more or until golden brown and cheese is melted.)