Spicy Summer Rolls with Peanut Dipping Sauce

INGREDIENTS

• 2/3 cup hoisin sauce (see Cooks' notes:)
• 1/3 cup creamy peanut butter
• 1/3 cup water
• 3 tablespoons fresh lime juice
• 1 1/2 tablespoons soy sauce
• 3 ounces dried rice-stick noodles
• 2 tablespoons fresh lime juice, divided
• 1 1/2 teaspoons sugar
• 2 3/4 cups coarsely grated carrot (about 1 pound; use large holes on a box grater)
• 3 tablespoons finely chopped serrano or jalapeño chiles, including seeds
• 12 (8-inch) rice-paper rounds, plus more in case some tear
• 4 cups thinly sliced napa cabbage, coarsely chopped
• 1 cup finely chopped cocktail peanuts
• 1 cup fresh mint leaves
• 1 cup fresh basil leaves (Asian or Italian)