1. Make sauce: stir together all sauce ingredients in a small bowl until sugar is dissolved.
2. Make rolls: add shrimp to a 4- to 5-quart pot of boiling salted water, then reduce heat and poach shrimp at a bare simmer, uncovered, until just cooked through, about 3 minutes.
3. Transfer shrimp with a slotted spoon to a bowl of ice and cold water to stop cooking, then return shrimp cooking water to a boil.
4. Chill shrimp in ice water 2 minutes, then drain and pat dry. Cut each shrimp in half lengthwise, deveining if necessary.
5. Add noodles to boiling water and cook until just tender, about 3 minutes.
6. Drain in a colander, then rinse under cold running water and drain well.
7. Stir together vinegar, sugar, and salt in a large bowl until sugar is dissolved, then add noodles and toss to coat.
8. Put a double thickness of paper towel on a work surface and fill a shallow baking pan with warm water. Check rice-paper rounds and use only those that have no holes. Soak 1 round in warm water until pliable, 30 seconds to 1 minute, then carefully transfer to paper towels.
9. Arrange 3 shrimp halves (cut sides up) in a row across bottom third (part nearest you) of soaked rice paper. Spread 1/4 cup noodles on top of shrimp and arrange 3 cilantro leaves, 3 mint leaves, 8 cucumber matchsticks, 6 scallion strips, and 10 mango matchsticks horizontally on top of noodles.
10. Fold bottom of rice paper over filling and begin rolling up tightly, stopping at halfway point. Arrange 3 more mint leaves and 3 more cilantro leaves along crease, then fold in ends and continue rolling.
11. Transfer summer roll, seam side down, to a plate and cover with dampened paper towels. Make 7 more rolls in same manner and serve, whole or halved diagonally, with dipping sauce.

Makes 8 first-course servings.

Make ahead: summer rolls can be made 4 hours ahead and chilled, covered with dampened paper towels and then with plastic wrap. Bring to room temperature before serving.

*Available at Asian markets and ethnicgrocer.com (866-438-4642).