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 1 minute until fragrant.
Add the ground beef to the skillet, breaking it apart with a spatula. Cook until browned and fully cooked, about 5-7 minutes.
Mix in the sliced bell pepper and broccoli florets, cooking for another 3-4 minutes until the vegetables are tender.
In a small bowl, whisk together the soy sauce, brown sugar, rice vinegar, 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, tossing everything together until the noodles are well coated with the sauce. Heat for an additional 2-3 minutes.
Serve hot, garnished with sliced green onions.