Combine chicken, fish sauce, 1 tablespoon sesame oil, and next 3 ingredients (through garlic) in a large zip-top plastic bag; seal and marinate in refrigerator 2 hours. Remove chicken from bag; reserve marinade.
Cook noodles according to package directions; set aside. Remove center stalks from bok choy and coarsely chop. Repeat procedure with bok choy leaves and set aside separately. Combine water and cornstarch; mix well and set aside.
Heat remaining 1 tablespoon oil in a wok or large nonstick skillet over medium-high heat. Add chicken; stir-fry 2 minutes. Transfer to bowl; set aside. Add reserved marinade, bok choy stalks, and mushrooms; stir-fry 3 minutes. Add bok choy leaves, chicken, and cornstarch mixture; stir-fry 2 minutes or until sauce thickens. Serve chicken mixture over noodles. Top with cilantro.