Cook noodles as directed on package. Drain; cover to keep warm.
Meanwhile, in small bowl, combine peanut butter, gingerroot, pepper flakes and 2 tablespoons of the soy sauce; beat with wire whisk until blended. Gradually beat in remaining soy sauce and water until smooth. Set aside.
Heat oil in 12-inch nonstick skillet over medium-high heat until hot. Add broccoli, mushrooms, carrots and bell pepper; cook 4 to 6 minutes or until vegetables are crisp-tender, stirring occasionally. Add chicken; cook and stir until thoroughly heated.
Reduce heat to medium. Stir peanut butter mixture; stir into mixture in skillet. Add cooked noodles; toss gently to coat. Cook and stir until thoroughly heated. Sprinkle with peanuts and cilantro.