Combine first 6 ingredients in a small bowl. Combine 1/4 cup broth mixture and chicken in a bowl. Reserve the remaining broth mixture.
Prepare noodles according to package directions, omitting salt; drain noodles, and keep warm.
Heat 1 teaspoon vegetable oil in a large nonstick skillet until hot. Add the chicken mixture, and stir-fry for 5 minutes or until done. Remove the chicken from pan, and keep warm. Heat 1 teaspoon vegetable oil in pan until hot. Add the broccoli and remaining ingredients, and stir-fry for 5 minutes or until crisp-tender. Return the chicken and reserved broth mixture to pan; cover and cook over medium heat for 2 minutes or until thoroughly heated. Serve over noodles.