Mix water, peanut butter, sugar, soy sauce, cornstarch, gingerroot and onions in medium bowl; set aside.
Spray 4-quart Dutch oven with cooking spray; heat over medium-high heat. Cook cauliflowerets, broccoli, carrots and celery in Dutch oven 5 minutes, stirring frequently. Stir in bean sprouts and water chestnuts. Cook 3 minutes, stirring frequently. Reduce heat to medium; stir in peanut butter mixture. Cover and cook about 5 minutes, stirring occasionally, until sauce is thickened.
Serve vegetable mixture over noodles. Sprinkle with peanuts.