Prepare noodles according to package instructions. Drain, toss in 1 tsp sesame oil, and set aside.
Prepare sauce by combining brown sugar, 4 tbsp soy sauce, Hoisin sauce, oyster sauce, black pepper, white pepper, and remaining 1 tsp sesame oil in a bowl and whisking until smooth. Set aside.
Slice cabbage, mushrooms, carrots, bell pepper, and broccoli into thin strips.
Slice chicken breast(s) into thin strips.*
Heat wok or large skillet pan on high heat with minced garlic, minced ginger, 2 tbsp light oil, and remaining 2 tbsp soy sauce. When hot, add chicken and cook until browned, stirring constantly, about 3-5 minutes. Remove and set aside.
Add vegetables to the hot wok/pan with remaining 2 tbsp light oil. Cook for 2-3 minutes or until colors become bright and crisp, stirring constantly.
Return chicken to the pan/wok. Add prepared sauce, stirring until everything is combined and sauce is thickened (about 1-2 minutes), and then remove from heat. Immediately add noodles to still-warm pan/wok and toss until coated.
Serve and garnish with sesame seeds or chopped green onions.