Begin by boiling a pot of water. Once it reaches a rolling boil, add the egg noodles and cook according to package instructions until al dente. Drain and set aside.
In a large skillet or wok, heat the vegetable oil over medium heat. Add the chopped onion and cook for about 2 minutes until translucent.
Add the minced garlic and ground beef to the skillet. Cook, stirring frequently, for about 5-7 minutes or until the beef is browned and fully cooked.
Add the broccoli and carrot slices to the skillet. Stir-fry for another 3-4 minutes until the vegetables are tender but crisp.
In a small bowl, mix the soy sauce, brown sugar, sesame oil, ground ginger, salt, and pepper. Pour this sauce over the beef and vegetable mixture in the skillet. Stir well to coat everything evenly.
Add the drained noodles to the skillet and toss gently to combine all ingredients. Cook for an additional 2 minutes, allowing the noodles to warm through and absorb the flavors.
Serve the dish hot, garnished with chopped green onions if desired.