In a bowl, season the chicken with pepper, salt and 1 tablespoon of sesame oil. Mix well and set aside.
In another bowl, combine the chicken broth, the remaining tablespoon of sesame oil, the soy sauce, the hoisin sauce and the cornstarch. Mix well and set aside.
Heat some oil in a wok or large skillet over medium-high heat. Add the chicken and cook until no longer pink inside, 3–4 minutes. Remove the chicken from the pan and set aside.
Add the garlic and ginger to the pan and cook until they start to brown.
Add the onions, bean sprouts and cabbage. Stir-fry until the vegetables are tender, then add the green part of the cabbage.
Return the cooked chicken to the pan, add the cooked noodles and the reserved sauce. Cook for 3 minutes, until everything is well coated with sauce.