Cook the rice vermicelli noodles according to package directions, then drain and rinse under cold water. Set aside.
Prepare the dipping sauce by stirring together the fish sauce, lime juice, sugar, minced garlic, and chopped chili in a small bowl until the sugar dissolves. Set the sauce aside for serving.
Fill a large shallow dish with warm water. Dip one rice paper wrapper in the water for a few seconds until it softens, then lay it flat on a clean surface.
Place two shrimp halves in a row across the center of the wrapper, followed by a lettuce leaf, a small portion of vermicelli, mint leaves, cilantro, cucumber matchsticks, and carrot matchsticks.
Fold the sides of the wrapper inward, then roll tightly from the bottom to enclose the filling. Repeat with the remaining wrappers and filling.
Arrange the finished rolls on a platter or pack them in a container for transport.