Cook the shrimp with boiling water. Drain the water and let them drain. Peel them when they are cold. Cut them crosswise into 2 slices. Set aside. (Note 2)
Soak the vermicelli in hot water for 2 minutes. Drain and set aside.
Wash the vegetables and cut the cucumbers and carrots into thin strips.
Prepare a large container or plate larger than the rice papers. Pour some warm water into it.
Soak one piece at a time in warm water for 2 seconds, picking them up immediately when they soften. (Note 3)
Lay them flat on a clean table and place lettuce, vermicelli, carrots and cucumbers in that order under the center line of the rice paper.
Place 3 leaves of basil or mint next to them.
Place 3 pieces of shrimp on the top line of the rice paper.
Fold the rice paper from the bottom to the vegetables, fold 2 sides inward, and then roll it up. The rice paper is sticky, it will seal itself.
Repeat steps to make the following rice paper rolls.
Serve immediately with peanut dip and NUOC CHAM (Vietnamese chili sauce).