Make rolls: Bring a pot of salted water to a boil. Add shrimp, bring back to a boil and cook until pink and firm, 2 to 3 minutes. Transfer shrimp to a paper towel-lined plate and pat dry. Cut each shrimp in half lengthwise. Keep water at a steady boil.
Add vermicelli to boiling water and cook, stirring, until softened, about 1 minute. Drain in a large colander and rinse under cold running water. Set aside, tossing occasionally.
Soak each rice paper in hot water to soften. Place on a clean cloth kitchen towel. Lay a row of shrimp along lower third of each paper. Top with equal amounts peanuts, herbs and carrots. Add a large pinch of vermicelli. Pull rice paper over filling. Roll, folding in sides as you go. Place on a platter, seam side down, and repeat with remaining ingredients. Cut rolls in half.
Make dipping sauce: Combine ingredients in a small bowl, stirring to dissolve sugar. Serve chilled or at room temperature.