Shrimp-and-Vegetable Summer Rolls

In a bowl, toss the carrots, onion, 1/4 cup plus 2 tablespoons of the vinegar, and 2 tablespoons of the sugar. Let stand until the vegetables soften, 30 minutes. Drain. In a glass bowl, mix the remaining vinegar, sugar, and garlic. Microwave at high power for about 30 seconds, until the sugar is dissolved. Add the fish sauce and set aside for 30 minutes; discard the garlic. Meanwhile, soak 1 rice paper at a time in hot water until pliable, about 10 seconds; transfer to a work surface. Set a cilantro sprig and lettuce leaf on the lower third of the rice paper and top with 3 shrimp halves. Top with some of the yellow pepper, vermicelli, and the pickled vegetables; roll up tightly, folding in the sides. Place the roll on a platter and repeat with the remaining ingredients. Halve the rolls and serve with the sauce for dipping.