Whisk together the soy sauce, hoisin sauce, oyster sauce, brown sugar, sesame oil, chili garlic sauce, and beef broth in a small bowl until smooth.

Stir the cornstarch with the water in a separate cup to create a slurry.

Heat the cooking oil in a large skillet or wok over medium-high heat until shimmering.

Add the ground beef and cook while breaking it apart with a wooden spoon until browned and slightly crispy around the edges.

Stir in the garlic and ginger and cook until fragrant and aromatic.

Add the carrot and cabbage and cook until slightly softened but still crisp.

Pour the prepared sauce into the skillet and stir well to coat the beef mixture evenly.

Add the cornstarch slurry and simmer for a few minutes until the sauce thickens into a glossy consistency.

Toss the cooked noodles into the skillet and mix thoroughly until every strand is coated with sauce.

Sprinkle in black pepper, green onions, and sesame seeds for added texture and flavor.

Serve immediately while hot and glossy with extra green onions on top.