In a medium bowl, combine the chicken with Shaoxing wine, cornstarch, and salt, massaging it thoroughly to ensure even coverage.
Mix together chicken broth, Shaoxing wine, oyster sauce, soy sauce, sugar, white pepper, and sesame oil in a small bowl until smooth.
Prepare the noodles by boiling them just shy of the recommended time, then rinse under cold water, drain well, and set aside. If using fresh noodles, briefly dunk them in boiling water for about a minute, drain completely.
Heat one tablespoon of oil in a large skillet over medium-high heat until shimmering; spread the chicken out without crowding. Cook until the underside is lightly golden, about 30 to 45 seconds, then flip and cook the other side until it loses all pinkness, about 30 to 45 seconds more. Remove the chicken and set aside.
Add the remaining tablespoon of oil to the pan, toss in the ginger and garlic, stirring intermittently to release their aromas.
Introduce the carrots and cabbage to the pan, stir-frying just until they begin to soften, roughly one minute. Add the noodles and give everything a few tosses with tongs.
Return the cooked chicken to the pan and pour the prepared sauce over all the ingredients. Toss everything together carefully with tongs to distribute the sauce evenly.
Stir in the sliced pepper and green onions, mixing until the sauce is soaked up. Serve immediately while hot.