In small bowl, mix mayonnaise and garlic. Spread 1 side of each bread slice with butter; spread mayonnaise mixture on unbuttered side. On each of 4 bread slices, buttered sides down, layer ham, apple, arugula, onion, cheese and remaining bread slices, buttered sides up.
Heat 12-inch nonstick skillet over medium-low heat 3 to 5 minutes. Place sandwiches in hot skillet; cook uncovered 6 to 9 minutes, turning once, until bread is crisp and cheese is melted.