In a large bowl, combine the shredded chicken, green and red cabbage, carrots, red bell pepper, cilantro, green onions, and edamame. Toss to mix.
In a separate bowl, whisk together peanut butter, soy sauce, rice vinegar, lime juice, honey, sesame oil, ginger, and garlic until smooth. Add water as needed to reach a pourable consistency.
Drizzle the peanut dressing over the salad and toss well to coat all ingredients evenly.
Sprinkle chopped peanuts on top for crunch.
Serve immediately or chill for 30 minutes for flavors to meld.
