Place noodles in a large bowl and cover with boiling water. Let stand until softened, about 4 minutes. Drain and rinse the noodles. Allow to cool.
While the noodles are cooling, whisk together the lime juice, tamari, rice vinegar, garlic chili paste, and toasted sesame oil in a small bowl.
If the noodles are long, you may want to cut them with kitchen scissors after they cool.
Place the noodles in a large bowl along the dressing and toss to combine. Add the edamame, carrots, mung bean sprouts, cucumber, basil, cilantro, scallions, and chili, and gently toss to combine.
Divide the noodles among 4 plates or bowls. Sprinkle with peanuts and sesame seeds. Garnish with lime wedges.