Begin by boiling the noodles according to the package directions. Once cooked, drain them and set aside.

In a large frying pan or wok, heat the canola oil over medium-high heat. Add the chopped onion and sauté for about 3 minutes until it becomes soft and translucent.

Incorporate the minced garlic and ground beef into the pan. Cook until the beef is browned and fully cooked, breaking it up with a spatula, which should take around 5-7 minutes.

Add the sliced bell peppers and broccoli florets to the pan. Stir-fry for an additional 3-4 minutes, allowing the vegetables to remain slightly crisp.

In a separate bowl, whisk together the soy sauce, hoisin sauce, toasted sesame oil, grated ginger, and chili flakes (if using). Pour this mixture over the beef and vegetables, stirring well to ensure everything is coated.

Toss the cooked noodles into the skillet, mixing thoroughly until the noodles are evenly distributed and heated through, about 2-3 minutes.

Serve immediately, garnishing with chopped green onions and sesame seeds if desired.