Cook the noodles: Boil according to package directions until just shy of al dente.
Drain, rinse briefly with cold water, and toss with a little oil to prevent sticking.
Make the sauce: In a bowl, whisk soy sauce, oyster sauce, hoisin, sesame oil, sugar, rice vinegar, broth, cornstarch, pepper, and optional chili. Set aside.
Prep the veggies: Have the cabbage, carrot, pepper, and green onions ready. Stir-fries move fast, so keep everything close to the stove.
Brown the chicken: Heat 1 tablespoon oil in a large wok or skillet over medium-high heat.
Add ground chicken and cook, breaking into small bits, until browned and cooked through, 4–6 minutes. Season lightly with a pinch of salt. Transfer to a plate.
Sauté aromatics: Add the remaining 1 tablespoon oil to the pan.
Stir in garlic, ginger, and the white parts of the green onions. Cook 30–45 seconds until fragrant, not burned.
Cook the vegetables: Add cabbage, carrot, and bell pepper. Stir-fry 2–4 minutes until crisp-tender.
If using bean sprouts, add during the last minute.
Combine: Return the chicken to the pan. Toss in the cooked noodles. Give the sauce a quick stir (cornstarch settles), then pour it over everything.
Toss and thicken: Stir-fry 1–2 minutes until the sauce thickens slightly and coats the noodles.
Add green onion tops. Taste and adjust salt, pepper, or heat.
Finish and serve: Remove from heat. Garnish with sesame seeds and extra green onions if you like.
Serve hot.