Make the sauce. In a bowl, whisk together the soy sauce, hoisin, oyster sauce, brown sugar, sesame oil, water or broth, cornstarch, pepper, and optional chili sauce.
Par-cook the noodles. Bring a large pot of water to a boil. Add the 4 noodle nests and cook for 3 minutes, stirring gently as they loosen. Drain well and rinse briefly with cold water to stop the cooking.
Brown the beef. Heat a wok or large skillet over medium-high heat. Add the ground beef and cook for 5–7 minutes, breaking it into small pieces, until browned and fully cooked. Drain off excess grease, leaving about 1 tablespoon in the pan if desired.
Stir-fry vegetables. Add oil only if the pan is dry. Add the onion, broccoli, and bell pepper; cook for about 3–4 minutes. Add garlic, ginger, and cabbage, then stir-fry for another 1–2 minutes until the cabbage softens slightly.
Add noodles and sauce. Stir the sauce again, pour it into the skillet, and bring it to a light simmer. Add the drained noodles. Toss continuously for 2–3 minutes, until the noodles are hot, evenly coated, and the sauce has thickened and mostly absorbed.
Finish and serve. Stir in green onions, taste, and add a small splash of soy sauce if needed. Serve immediately.
