Remove the yakisoba noodles from the package, and transfer to a bowl of hot water. Gently break them up; the hot water will help loosen them. Drain thoroughly and set aside.
In a small bowl, mix together the soy sauce, oyster sauce, mirin, Worcestershire sauce, and sugar until thoroughly combined. In a separate bowl, combine the sliced chicken with 2 teaspoons cornstarch and 2 teaspoons oil. Set aside.
Heat 1 tablespoon of oil in a wok over high heat. Add the chicken in one layer and allow to sear for 1 minute. Stir-fry for another minute, remove from the wok, and set aside.
Add 2 tablespoons of oil to the wok, along with the shiitake mushrooms. Stir-fry for 2 minutes and then add the onions, carrots, and cabbage. Stir-fry for another 2 minutes, and then add the noodles, seared chicken, scallions, and the sauce mixture. Continue to stir-fry the mixture for another 2-3 minutes until the noodles are heated through. Serve!