Soak rice noodles in very hot water until tender, 4–6 minutes; drain and rinse cool.
Whisk peanut butter, soy sauce, lime juice, vinegar, sugar, garlic, ginger, chili paste, and sesame oil.
Stir in warm water until the sauce is silky and dippable.
Arrange fillings on a platter; fill a wide bowl with warm water.
Dip one rice paper briefly to soften, then place on a damp board.
Layer lettuce, noodles, shrimp, carrots, cucumber, bell pepper, herbs, and scallions across the center.
Fold sides in, then roll tightly from the bottom to enclose.
Repeat with remaining wrappers and fillings.
Serve whole or halved with peanut sauce on the side.