Prep the vegetables and aromatics: mince the garlic and ginger; thinly slice the onion, celery, carrot, and cabbage; cut the scallions into 2-inch pieces; rinse and drain the bean sprouts.
Marinate the chicken: in a bowl, toss the sliced chicken with the Shaoxing wine and cornstarch until evenly coated; set aside for 10 minutes while you prepare the sauce.
Make the sauce: in a measuring cup or small bowl, whisk together the oyster sauce, light soy sauce, dark soy sauce, chicken stock, granulated sugar, white pepper, and sesame oil until smooth; keep near the stove.
Cook the noodles: bring a large pot of water to a boil, add the chow mein noodles, and cook until just tender but still springy (follow package timing; usually 2–4 minutes). Drain well and shake off excess water; set aside.
Stir-fry the chicken: heat a wok or large skillet over high heat until very hot, then add 1.5 tablespoons neutral oil. Spread the marinated chicken in a single layer and sear, stirring once or twice, until opaque and just cooked through, 3–4 minutes. Transfer to a plate.
Stir-fry aromatics and vegetables: return the wok to high heat and add the remaining 1.5 tablespoons neutral oil. Add the garlic and ginger; stir-fry until fragrant, about 10 seconds. Add the onion, celery, carrot, and cabbage; stir-fry until crisp-tender with light char in spots, 2–3 minutes.
Combine and sauce: add the drained noodles, the cooked chicken (with any juices), the bean sprouts, and the scallions to the wok. Pour in the sauce and toss constantly with tongs or chopsticks until the noodles are evenly coated, the vegetables are crisp-tender, and the sauce reduces to a glossy sheen that clings lightly, 1–2 minutes.
Serve immediately while hot and steamy, with the noodles bouncy, the chicken tender, and the vegetables still vibrant and crunchy.