How to Make It
In a large bowl, mix 3 tablespoons of the fish sauce with 3 tablespoons of the lime juice and the sugar and stir until the sugar is dissolved. Add the papaya, carrots, cilantro and mint and toss to combine.
Fill a large bowl halfway with cold water. One at a time, submerge the rice paper wrappers in the water and let soak together for 5 minutes, or until pliable.
Meanwhile, in a blender, puree the coconut milk with the peanuts, water, hoisin sauce, garlic and the remaining 1/2 tablespoon each of fish sauce and lime juice. Transfer the dipping sauce to a bowl and season lightly with salt.
Set a strainer over a bowl and drain the papaya salad well. Divide the salad into 6 portions. Drain the rice paper wrappers and pat dry. Arrange 3 wrappers on a dry work surface, keeping the rest covered with a damp towel. Arrange 3 shrimp halves in a neat row, facing the same direction, just below the center of each wrapper; top with the papaya salad and 3 more shrimp halves. Fold the bottom edge of the wrappers over the filling and roll them into tight cylinders, tucking in the sides as you roll. Transfer the finished rolls to a plate and cover. Repeat to form the remaining 3 rolls. Serve the summer rolls with the dipping sauce on the side.