In a medium bowl, combine the chicken with Shaoxing wine, cornstarch, and salt, ensuring the meat is well coated.
Mix the chicken broth, Shaoxing wine, oyster sauce, soy sauce, sugar, white pepper, and sesame oil in a small bowl to create the sauce.
Cook the chow mein noodles according to instructions until just tender, rinse with cold water, drain thoroughly, and set aside.
Heat one tablespoon of oil over medium-high heat in a large skillet until shimmering, then arrange the chicken pieces in a single layer.
Sear the chicken until the bottoms are lightly browned, about 30 to 45 seconds, then flip and cook the other side until the chicken turns opaque; remove and set aside.
Add the remaining oil, ginger, and garlic to the pan, stirring briefly to release aromas.
Toss in the carrots and cabbage, stir-frying until they begin to soften, roughly 1 minute.
Introduce the noodles to the skillet and toss gently with the vegetables.
Return the cooked chicken to the pan and drizzle the prepared sauce over everything, mixing thoroughly with tongs to coat all ingredients.
Add the sliced pepper and green onions, continuing to toss until the sauce is absorbed.
Serve the chow mein hot, dividing it among plates as a hearty main dish.