Preheat broiler with oven rack in middle position.
Spread each bread slice with 1 teaspoon mayonnaise and 1 teaspoon mustard. Layer each slice with 1/4 cup arugula, 1 onion slice, 3 ounces turkey, 4 apple slices, and 2 tablespoons cheese.
Place sandwiches on a baking sheet; broil 4 minutes or until cheese is bubbly. Remove from heat; sprinkle with pepper, if desired. Serve immediately.