Cook the egg noodles according to package instructions. Drain and set aside.

In a large skillet or wok, heat the vegetable oil over medium-high heat. Add the diced onion and sauté for 2-3 minutes until translucent.

Add the minced garlic and cook for an additional 30 seconds until fragrant.

Add the ground beef to the skillet, breaking it apart with a spatula. Cook until browned, about 5-7 minutes. Drain excess fat if necessary.

Stir in the broccoli florets and sliced bell peppers. Cook for 3-4 minutes until the vegetables are tender-crisp.

In a small bowl, whisk together the soy sauce, brown sugar, cornstarch, beef broth, ground ginger, and black pepper. Pour this mixture over the beef and vegetables in the skillet.

Stir well to combine and cook for another 2-3 minutes until the sauce thickens.

Add the cooked egg noodles to the skillet, tossing everything together until the noodles are well coated with the sauce.

Serve hot, garnished with sliced green onions and sesame seeds if desired.