In a large mixing bowl, add the Napa cabbage, red cabbage, shredded chicken, carrots, red pepper, green onions, and chopped cilantro. Gently toss to combine.
In a food processor or small blender, combine the rice vinegar, soy sauce, creamy peanut butter, honey, sesame oil, garlic, and ginger. Blend until smooth and fully emulsified. Adjust seasoning with salt if necessary.
Drizzle the prepared dressing over the cabbage and chicken mixture. Toss well to ensure all components are evenly coated.
Portion the salad into four individual serving bowls. Garnish each with a generous handful of crunchy chow mein noodles just before serving.