1. Bring 2 1/2 quarts of lightly salted water to a boil in a covered 4 1/2-quart or larger pot. When the water reaches a rapid boil, add the pasta and cook until just tender, according to the package directions.
2. Meanwhile, if the chicken is frozen, run it under hot water so you can remove any packaging. Place the chicken on a microwave-safe plate, and microwave 2 minutes, uncovered, on high, to begin defrosting. Meanwhile, pour the frozen broccoli in a colander and run warm tap water over it to begin defrosting. Set aside to drain.
3. Heat the oil on medium in an extra-deep, 12-inch skillet. Peel and coarsely chop the onion, adding it to the skillet as you chop. Stir from time to time. While the onion cooks, cut the chicken (fresh or partially defrosted) into bite-size pieces. When all of the chicken is cut, add it to the skillet.
4. Add the sliced mushrooms, broccoli, garlic and ginger. Cook, stirring frequently, until the mushrooms release their liquid and the chicken is no longer pink in the center, about 4 to 5 minutes.
5. Add the soy sauce, vinegar, ketchup, and sesame oil to the skillet. Stir well to blend. Remove the skillet from the heat.
6. When the noodles are done, drain them well (using the same colander that held the broccoli), and add them to the skillet. Stir until the noodles are coated with sauce and combined with the vegetables. Serve at once. Serves 4.
**You can use 3 cups of Chunky Seasoned Chicken, defrosted if frozen. Skip step 3 above.