Cook pasta as directed on package, adding broccoli to the boiling water for the last 3 minutes of the pasta cooking time.
Meanwhile, spray large nonstick skillet with cooking spray; heat on med-high heat. Add chicken; cook 6-8 minutes or until cooked through, stirring occasionally. Stir in dressing, soy sauce, ginger, garlic, and crushed red pepper; cook 1 minute, stirring occasionally.
Drain pasta mixture; place in large bowl. Add chicken mixture; mix lightly. Spoon evenly into 4 serving bowls; sprinkle with peanuts.