Boil the egg noodles according to the package directions. Once cooked, drain and set aside.
In a large skillet or wok, heat the canola oil over medium-high heat.
Add the chopped onion and sauté until soft and translucent, about 3-4 minutes.
Incorporate the minced garlic and sliced bell peppers, stirring for another 2-3 minutes until softened.
Create a space in the center of the skillet and add the ground beef. Cook until fully browned, breaking it apart with a spatula, about 5-7 minutes.
In a separate bowl, mix together the soy sauce, brown sugar, cornstarch, beef broth, ground ginger, and black pepper until smooth.
Pour the sauce over the beef and vegetables in the skillet, stirring well to combine. Allow to simmer for 3-5 minutes to thicken.
Add the cooked egg noodles and broccoli florets to the skillet, tossing everything together until well mixed.
Cook for an additional 2-3 minutes until everything is heated through.
Serve immediately, garnished with chopped green onions and a sprinkle of sesame seeds if desired.