Make the peanut sauce: Combine the peanut butter, water, honey, lime juice, and sesame oil in a small saucepan over medium heat. Stir until smooth and creamy. Set aside to cool.
Cook the noodles: Cook the rice vermicelli according to the package instructions. Drain, rinse under cold water, and set aside.
Cook the shrimp: Cook the shrimp until pink and opaque, about 2 minutes per side. Let cool slightly.
Prepare the fillings: Julienne the mango, carrot, and cucumber. Slice the green onions and wash the lettuce, mint, and cilantro.
Soften the rice paper: Dip one rice paper wrapper in lukewarm water for 5–10 seconds until flexible but not completely soft. Place it on a clean work surface.
Fill and roll: Layer a little lettuce, rice vermicelli, vegetables, herbs, and shrimp in the center of the wrapper. Fold the bottom edge over the filling, fold in the sides, then roll tightly to seal.
Repeat and serve: Repeat with the remaining ingredients. Serve immediately with the peanut sauce for dipping.