Bring a large pot of water to a rolling boil and cook noodles according to package instructions, reducing time by 1-2 minutes. Drain, rinse with cold water, shake well, and toss with 1 tablespoon sesame oil to prevent sticking.
In a medium bowl, combine sliced chicken with 1 tablespoon light soy sauce, 1 teaspoon cornstarch, 1 teaspoon neutral oil, and 1/4 teaspoon white pepper. Toss to coat thoroughly and let marinate for 10-15 minutes at room temperature.
In a small bowl, whisk together 3 tablespoons light soy sauce, 1 tablespoon dark soy sauce, 2 tablespoons oyster sauce, 1 teaspoon sesame oil, 1 teaspoon sugar, 1/4 teaspoon white pepper, and 2 tablespoons water. Set aside.
Julienne the carrot, thinly slice the bell pepper and cabbage, separate green onion whites from greens, and mince the garlic and ginger. Arrange all ingredients on a tray ready for quick addition to the wok.
Heat wok over high heat until smoking. Add 1 tablespoon oil, then add chicken in a single layer. Sear for 1-2 minutes without moving, flip, and cook another 1-2 minutes until golden and cooked through. Remove to a plate.
Return wok to high heat and add remaining 1 tablespoon oil. Add garlic, ginger, and white parts of green onions, stir-frying 30 seconds until fragrant. Add carrots and stir-fry 1-2 minutes, then add bell pepper and cabbage and cook 2-3 minutes until crisp-tender.
Add cooked noodles and seared chicken to the wok. Pour sauce evenly over everything and toss vigorously with tongs over high heat for 1-2 minutes until sauce coats all noodles evenly and appears glossy.
Remove from heat, scatter green onion greens over top, and toss once more. Transfer to serving bowls, garnish with sesame seeds and extra green onions if desired, and serve immediately.