Prepare the Beef : Combine the beef slices with the marinade ingredients: Shaoxing wine, cornstarch, and salt. Mix well and let it sit for 15 minutes to tenderize the meat.
Cook the Noodles : Cook the egg noodles according to the package instructions. Drain and toss with 1 tablespoon sesame oil to prevent sticking. Reserve 2 tablespoons of the cooking water for the sauce.
Prepare the Sauce : In a small bowl, whisk together the beef broth, light soy sauce, oyster sauce, Shaoxing wine, cornstarch, sugar, and reserved noodle water. Set aside.
Stir-Fry the Protein : Heat 1 tablespoon of sesame oil in a large wok or skillet over medium-high heat. Add the marinated beef and stir-fry until browned and cooked through, about 2-3 minutes. Remove and set aside. Add the shrimp to the same pan and stir-fry until pink and cooked, about 2 minutes. Remove and set aside with the beef.
Cook the Vegetables : Heat another tablespoon of sesame oil in the wok. Add garlic, ginger, and onion, stir-frying until fragrant. Add bok choy and carrot, stir-frying until tender but still crisp, about 3-4 minutes.
Combine and Stir-Fry : Return the cooked beef and shrimp to the wok. Add the cooked noodles and pour the prepared sauce over the mixture. Toss everything together until well-coated in the sauce and heated through, about 2 minutes.
Finish and Serve : Drizzle with a touch of sesame oil for extra aroma, and serve hot. Enjoy your homemade Hong Kong noodles with a side of chili sauce or soy sauce if desired.