To prepare sauce, combine vinegar, honey, fish sauce, and curry paste, stirring with a whisk. Set aside.
To prepare rolls, cook rice sticks according to package directions; drain and rinse under cold water. Drain.
Trim fibrous ribs from lettuce leaves to flatten leaves.
Add hot water to a large, shallow dish to a depth of 1 inch. Place 1 rice paper sheet in dish; let stand 30 seconds or until soft. Place sheet on a flat surface. Arrange 1 lettuce leaf over sheet. Top lettuce with 2 basil leaves, 4 shrimp halves, 2 tablespoons noodles, 5 cucumber strips, 5 carrot strips, 5 green onion strips, and 3 mint leaves. Fold sides of sheet over filling, and roll up jelly-roll fashion. Gently press seam to seal. Place roll, seam side down, on a serving platter (cover to prevent drying). Repeat procedure with remaining rice sheets, lettuce, basil, shrimp, noodles, cucumber, carrot, green onion tops, and mint. Serve with the sauce.