Prep vegetables and herbs: Prepare the carrot and cucumber by cutting them into thin julienne. Thinly slice the red bell pepper. Rinse and drain the bean sprouts well. Tear the green leaf lettuce to fit the wrappers. Pick the fresh mint leaves, fresh cilantro leaves, and fresh Thai basil leaves from their stems and pat dry.
Cook the rice vermicelli noodles in a large pot of boiling water until tender but still springy, 3–4 minutes; drain and rinse under cold water, then drain very well so the rolls don’t become soggy.
Set up a rolling station with a large shallow dish of warm water, a clean damp kitchen towel or board, the noodles, the prepared vegetables and herbs, and the cooled sauce.
Soften a rice paper wrapper by dipping it in warm water for 5–10 seconds until pliable but not limp; lay it smooth-side down on the damp towel.
Build each roll: Near the lower third of the wrapper, place a piece of lettuce, a small nest of noodles, and a neat line of the prepared vegetables and herbs. Fold the bottom of the wrapper up over the filling, fold in the sides, and roll tightly into a cylinder.
Repeat with the remaining wrappers and fillings to make 12 rolls.
Right before serving, top the peanut sauce with the roasted peanuts (for serving). Serve the rolls immediately with the peanut sauce for dipping.