Cook the chow mein noodles according to the package directions.
Drain and rinse with cold water. Set aside.
In a small bowl, whisk together the soy sauce, oyster sauce, hoisin sauce, sesame oil, brown sugar, cornstarch, chicken broth, and black pepper.
Heat 1 tablespoon vegetable oil in a large skillet or wok over medium-high heat.
Add the chicken and cook for 5 to 6 minutes until browned and fully cooked.
Transfer the chicken to a plate.
Add the remaining oil to the skillet.
Cook the garlic and ginger for 30 seconds.
Add the cabbage and carrots and stir-fry for 3 to 4 minutes until slightly tender.
Stir in the bean sprouts and green onions.
Return the chicken to the skillet.
Add the cooked noodles.
Pour the sauce over everything.
Toss well until evenly coated and cook for 2 to 3 minutes until heated through.
Serve immediately.