Boil the egg noodles in a large pot according to the package directions. Once cooked, drain and set aside.
In a large frying pan, heat the canola oil over medium heat. Add the chopped onion and sauté for about 3 minutes until soft and translucent.
Incorporate the minced garlic and continue cooking for another minute until fragrant.
Raise the heat to medium-high and add the ground beef, cooking thoroughly for about 5 to 7 minutes until browned.
Add the broccoli and bell pepper, cooking for an additional 3 to 4 minutes until tender yet crisp.
In a separate bowl, mix together the soy sauce, brown sugar, cornstarch, beef broth, ground ginger, and crushed red pepper (if using).
Pour the sauce mixture over the beef and vegetables, stirring well to coat. Let it simmer for 2 to 3 minutes until the sauce thickens slightly.
Add the drained egg noodles to the skillet, gently tossing to coat in the sauce. Heat through for another minute.
Serve immediately, garnished with chopped green onions and sesame seeds.