Marinate the chicken: In a medium bowl, whisk together 1 tablespoon soy sauce, 1 tablespoon corn starch, and 1 tablespoon vegetable oil. Add the chicken cut into small, bite-sized pieces. Season the chicken with black (or white) pepper. I'm not adding any salt because the soy sauce is already salty. Toss to coat and set aside.
Cook the noodles according to the package instructions. I cook mine always 1 minute shorter to ensure they are not overcooked (they will be cooked briefly later with the sauce). Spread the cooked noodles on a large plate or baking sheet lined with kitchen towels to dry them out a bit.
Make the sauce: whisk all the ingredients for the sauce in a medium bowl.
Chop the vegetables: cut the carrot into matchsticks, slice the mushrooms into thin slices, cut the cabbage into thin slices. Slice the green onions: white part into thin slices and the dark green park into large chunks. Reserve some green onions for the garnish (the dark green parts). Finely chop the garlic.
Cook the chicken: Heat a large frying pan over high heat. When hot add the oil. When the oil is hot add the chicken. Don't stir for the first 1-2 minutes letting the chicken brown, the cook, stirring, for a couple of minutes until the chicken is cooked through. Add the garlic and cook for 30 seconds. Transfer the chicken to a plate.
Cook the vegetables: Add another tablespoon of oil and all the vegetables to the pan. Cook over medium-high heat for a couple of minutes until softened but still crunchy.
Assemble: Add the chicken back to the pan, add the sauce and noodles. Let the sauce come to a boil then stir everything together until evenly coated. If your pan is too small you can transfer all the ingredients into a large pot to stir them together comfortably.
Sprinkle with thinly sliced green onions.