In a large bowl, combine chicken strips with soy sauce, sesame oil, and cornstarch. Mix well and let marinate for at least 15 minutes while you prepare other ingredients.

In a small bowl, whisk together soy sauce, dark soy sauce, oyster sauce, rice vinegar, sugar, white pepper, cornstarch, and water/chicken broth until smooth. Set aside.

Bring a large pot of salted water to a rolling boil. Add chow mein noodles and cook according to package directions until al dente (usually 2-4 minutes for fresh, 5-7 for dried). Drain well, rinse with cold water to prevent sticking, and toss with 1 tsp of vegetable oil. Set aside.

Heat 1 tbsp of vegetable oil in a large wok or skillet over medium-high heat. Add marinated chicken and stir-fry until cooked through and lightly browned, about 3-5 minutes. Remove chicken from the wok and set aside.

Add the remaining 1 tbsp of vegetable oil to the wok. Add carrots, cabbage, and yellow onion. Stir-fry for 2-3 minutes until slightly tender-crisp. Add snow peas, minced garlic, and grated ginger. Stir-fry for another 1-2 minutes until fragrant.

Return the cooked chicken to the wok with the vegetables. Add the cooked noodles and bean sprouts. Give the prepared chow mein sauce another quick whisk and pour it over the noodles and vegetables. Toss everything together vigorously using tongs or spatulas, ensuring the sauce coats all ingredients evenly, for 2-3 minutes until the sauce thickens and everything is well combined and heated through.

Transfer the Chicken Chow Mein to serving plates. Garnish with sliced green onions and serve immediately.