Add all dressing ingredients to a blender. Blend until smooth. Set aside.
In a large bowl, combine cabbage, broccoli slaw, snow peas, carrots, and scallions.
Coat a large, nonstick pan with cooking spray. Add oil and heat over medium-high heat. Add ginger, garlic and cook for 30 seconds. Stir in broccoli/cabbage mixture, 3 tablespoons rice vinegar, 2 tablespoons soy sauce, and black pepper. Cook for about 5 minutes until soft-crisp.
Stir in chicken and peanut sauce. Mix well. Continue to stir-fry for a few minutes, until hot.