Heat broiler. On a baking sheet, toss turkey slices with olive oil, salt, and pepper. Broil until cooked through, 6 to 8 minutes. Transfer to a plate; wipe sheet with paper towels.
In a bowl, combine apple mostarda and mustard. Place bread slices on sheet. Layer 4 slices with mostarda mixture, turkey, Havarti cheese, and apple.
Broil until cheese melts and bread is toasted, 5 minutes. Top with lettuce and remaining toast.