Put noodles in a large bowl. Pour enough hot water over to cover; let stand until softened, about 10 minutes. Drain. Transfer to a large bowl to cool; set aside.
Fill a pie plate with warm water. Working with 1 rice paper round at a time, soak rice paper in water, turning occasionally until just pliable but not limp, about 30 seconds. Transfer to a work surface. Arrange 3 shrimp halves across center of round. Top with some leaves of each herb, then daikon sprouts, cucumber, and carrot. Arrange a small handful of noodles over. Place 1 lettuce leaf over, torn or folded to fit. Fold bottom of rice paper over filling, then fold in ends and roll like a burrito into a tight cylinder. Transfer roll, seam side down, to a platter.
Repeat to make 11 more rolls. Can be made 1 hour ahead. Cover with a damp kitchen towel and refrigerate. To serve, cut rolls in half on diagonal. Add chopped Chinese parsley to dipping sauce. Makes 12 rolls.
In a medium bowl, mix all ingredients. Can be made a day ahead. Cover and chill.
Tip: Vietnamese spring rolls are best eaten fresh but will last up to two days in the refrigerator. Bring to room temperature for about 30 minutes before eating.
Approximate Nutrient Analysis per serving:
160 calories, 1 g fat, 0 g saturated fat, 15 mg cholesterol, 550 mg sodium, 32 g carbohydrate, 6 g fiber, 8 g sugar, 9 g protein