1. Preheat broiler.
2. Combine mayonnaise and 1 teaspoon mustard; spread mayonnaise mixture over each bread slice. Top each slice with 1 tablespoon shallot, 1 ounce ham, and 4 teaspoons cheese, and sprinkle evenly with 1/4 teaspoon pepper. Broil 3 minutes. Combine 1 teaspoon mustard, oil, and vinegar. Combine the arugula and apple slices in a bowl; drizzle with vinaigrette. Toss gently. Divide the apple mixture evenly among sandwiches, and sprinkle with remaining 1/4 teaspoon pepper.