Cook the vermicelli noodles briefly in boiling water, adhering to the directions on the package. Once done, drain them and rinse under cold water to halt the cooking process.
Arrange all filling components—herbs, sliced vegetables, and shrimp—so they are ready for assembly.
Fill a deep dish or pie plate with about an inch of water. Submerge one rice wrapper in the water for 10 to 15 seconds, removing it while still slightly firm, then lay it flat on a clean surface.
Place a small portion of noodles, a few shrimp, strips of mango, carrot, and cucumber, and a few mint, basil, and cilantro leaves onto the lower third of the wrapper.
Begin by folding the left and right edges inward, then roll the bottom edge up over the fillings, continuing to roll tightly like a burrito to seal.
For the sauce, place all ingredients in a blender or food processor and blend until a smooth consistency is achieved.