Cook the noodles until al dente in a pot of boiling water according to package directions, and then drain.
Toss together the cilantro leaves, bell peppers, 1 tablespoon of the lime juice, the salt, carrots, cucumber and noodles in a large bowl. Stir together the peanut butter, honey, chopped cilantro, 3 tablespoons warm water and the remaining 2 tablespoons lime juice in a small bowl.
Working with 1 spring roll skin at a time, soak it in a pan of tepid water until soft and pliable, about 30 seconds. Lift it out and place on a work surface. Spoon some of the noodle-vegetable mix onto the end of the spring roll skin closest to you. Roll it away from you once, enclosing the mixture, then fold the sides over the filling and roll the spring roll up. Repeat with the remaining spring roll skins and filling and serve with the peanut sauce.