In a large saucepan of boiling salted water, cook the rice noodles until they are al dente, about 5 to 7 minutes; see package instructions. Drain and rinse them under running water until cold.
In a blender or food processor, combine the coarsely chopped ginger with scallions and smashed garlic and pulse until chopped. Add the fish sauce, lime juice and sugar and process until smooth.
Transfer the rice noodles to a large serving bowl. Add the chicken, tofu, carrots, cucumber, cilantro and mint and toss. Add the dressing and toss until evenly coated. Sprinkle the rice noodles with peanuts and serve with lime wedges if desired.