Spread 1/2 tsp. mayonnaise on each bread slice and 1/2 tsp. mustard on other side. Sprinkle half of cheese over mustard side of 4 slices. Add apple, spinach and remaining cheese. Top with remaining bread slices, mustard-side down.
Put 2 sandwiches in skillet; weigh down with another skillet. Cook until toasted, about 3 minutes. Turn sandwiches over, weigh down again and cook until cheese melts, about 3 minutes more. Transfer to a plate. Repeat to make other 2 sandwiches.