Cook the egg noodles according to package instructions. Drain and set aside.
In a large skillet, heat the vegetable oil over medium heat.
Add the diced onion and cook until translucent, about 3-4 minutes.
Stir in the minced garlic and cook for an additional 30 seconds.
Add the ground beef to the skillet, breaking it apart with a spatula, and cook until browned, about 5-7 minutes. Drain excess fat if necessary.
Stir in the sliced bell pepper and broccoli florets, cooking until the vegetables are tender, about 4-5 minutes.
In a small bowl, whisk together the soy sauce, brown sugar, hoisin sauce, ground ginger, and black pepper.
Pour the sauce over the beef and vegetable mixture, stirring to combine.
Add the cooked egg noodles to the skillet, tossing everything together until the noodles are evenly coated in the sauce.
Cook for an additional 2-3 minutes to heat through.
Serve hot, garnished with sliced green onions.