In a large pot, bring water to a boil and cook the egg noodles according to package instructions. Drain and set aside.
Heat a large skillet over medium-high heat. Add ground beef and cook until browned and cooked through, breaking it apart with a spoon. Drain excess fat if necessary.
Stir in minced garlic and grated ginger to the beef. Sauté for about 2 minutes until fragrant.
Add sliced bell pepper and julienned carrot to the skillet, cooking for another 3-4 minutes until the vegetables are tender.
In a small bowl, combine soy sauce, hoisin sauce, sesame oil, brown sugar, and beef broth. Stir well.
Pour the sauce over the cooked beef and vegetables, mixing well to coat everything evenly. Let it simmer for about 5 minutes.
Add the cooked pasta to the skillet, tossing gently to combine all ingredients. Season with salt and pepper to taste.
Once everything is heated through, sprinkle chopped green onions and sesame seeds on top. Serve immediately.
Notes
Feel free to add more vegetables or adjust the sauce ingredients to taste.