Bring a large pot of water to a rolling boil. Add the noodles and cook until just tender according to the package directions. Drain thoroughly and rinse with cool water to halt further cooking. Set aside.

Warm the oil in a large wok or deep skillet set over medium-high heat. Add the ground beef, using a spatula or wooden spoon to break it apart. Sauté until fully browned. If necessary, drain off any surplus fat.

Incorporate the garlic, grated ginger, and the white portions of the chopped green onions into the browned beef. Stir continuously for 1 to 2 minutes, allowing the aromatics to release their fragrance.

Toss in the shredded cabbage, carrot strips, and sliced red bell pepper. Stir-fry for 3 to 4 minutes, or until the vegetables begin to soften but still retain a slight crunch.

In a separate mixing bowl, whisk together the soy sauce, oyster sauce, hoisin sauce, brown sugar, sesame oil, beef broth, and black pepper until well combined.

Introduce the drained noodles into the skillet, layering them over the beef and vegetables. Pour the prepared sauce mixture on top and toss thoroughly to ensure even coating. Continue to cook for 2 to 3 additional minutes until everything is heated through.

Remove the pan from heat. Garnish the dish with the green tops of the scallions and, if desired, a sprinkling of sesame seeds. Serve immediately while hot.