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 sliced bell pepper to the skillet. Cook for another 2 minutes, stirring frequently.
Add the ground beef to the skillet, breaking it apart with a spatula. Cook until browned and fully cooked, about 5-7 minutes.
Stir in the broccoli florets and cook for an additional 3-4 minutes until the broccoli is tender.
In a small bowl, mix together the soy sauce, brown sugar, hoisin sauce, ground ginger, and black pepper. Pour this sauce over the beef and vegetable mixture, stirring to combine.
Add the cooked egg noodles to the skillet and toss everything together until the noodles are well coated with the sauce. Cook for another 2-3 minutes to heat through.
Serve hot, garnished with sliced green onions.