Prepare all your ingredients by dicing the onion, mincing the garlic, slicing the bell pepper, and breaking the broccoli into florets.
In a large skillet, heat the vegetable oil over medium heat. Add the diced onion and sauté for 2-3 minutes until soft. Then, add the minced garlic and ground beef, cooking until browned.
Add the sliced bell pepper and broccoli florets to the skillet and cook for an additional 5 minutes. Mix together the soy sauce, brown sugar, hoisin sauce, ground ginger, and black pepper in a bowl, then pour over the beef and vegetables.
Prepare the egg noodles according to the package instructions, then drain and set aside.
Add the cooked egg noodles to the skillet with the beef and vegetable mixture, tossing gently to coat. Cook for another 2-3 minutes to heat through.