Cook the noodles according to package instructions. Drain and set aside.
In a small bowl whisk all the sauce ingredients together, then set aside.
In another medium sized bowl toss together the chicken with the soy sauce, ginger and garlic.
Heat 2 tablespoons of olive oil well in a large wok. Your wok should be nice and hot before adding the chicken to it. Add the seasoned chicken and cook for about 5 minutes or until the chicken starts to brown and is no longer pink inside. Transfer chicken to a plate and set aside. Don't overcrowd the chicken, you might need to do this in 2 batches.
Add the other 2 tablespoons of olive oil to the wok then add the shiitake mushrooms, cabbage, carrots and onion to the wok. Cook for a minute while tossing around.
Add the chicken back to the wok. Add the cooked noodles, prepared sauce and toss everything together. Turn off the heat.
Garnish with green onions and serve.
