In a large skillet, heat the oils over medium-high heat. Add the chicken and cook for 4 to 5 minutes or until lightly browned. Add broccoli, mushrooms, carrots, pepper, and onion and cook an additional 5 minutes, stirring frequently. Stir in the water chestnuts. In a small bowl, combine broth, hoisin sauce, soy sauce, ginger, and cornstarch. Add to chicken mixture and bring to a boil over medium-high heat. Reduce heat to medium to medium-low, and simmer for 4 to 5 minutes, or until sauce thickens. Serve over hot, cooked rice noodles.