Place noodles in a large bowl and cover with hot water. Set aside until noodles are softened, about 15 minutes. Drain and rinse thoroughly.
Fill a shallow baking dish with hot water. Soak 1 rice paper in the hot water until softened, 5 to 10 seconds. Lay flat on a work surface. Place a thin layer of rice noodles, iceberg lettuce, bean sprouts, daikon, cabbage, carrots, cucumber, mizuna, and Thai basil near the top. Fold in sides and roll up rice paper to enclose the filling. Repeat with remaining rice wrappers.
Mix hoisin sauce and applesauce together in a small bowl. Serve alongside rolls.