Cook the noodles according to the package instructions. Drain and rinse under cold water to stop cooking. Set aside.
Prepare the Dressing:In a medium bowl, whisk together the peanut butter, soy sauce, rice vinegar, sesame oil, honey or maple syrup, lime juice, and warm water. Adjust consistency with more water if needed—it should be pourable but not too thin.
In a large mixing bowl, combine the cooked noodles, shredded carrot, red bell pepper, purple cabbage, edamame, chicken, and green onions.
Pour the dressing over the noodle and vegetable mixture. Toss until everything is evenly coated.
Divide the noodle bowl into serving dishes. Top with chopped cilantro and peanuts if desired. Serve immediately, or chill in the fridge for a cold noodle salad.
