In a bowl, combine the sliced beef with 1 tablespoon of cornstarch and toss well until every piece is well coated with the cornstarch. Set aside.
In a mixing bowl, combine the garlic, ginger, soy sauce, honey, chicken broth, sesame oil, and black bean paste and mix well. In a separate mixing bowl, combine 1 tablespoons of cornstarch with 2 tablespoons of water. Add the cornstarch slurry into the sauce mixture and mix well. Set aside.
In a skillet, heat the canola oil over medium high eat. Stir fry the beef for about 3-5 minutes, or until cooked thoroughly. Remove from heat and set aside.
On the same skillet, stir fry the onions and broccoli florets until the onions are soft and fragrant, and the broccolis are soft but still a little bit crunchy, about 5 minutes. To cook the broccoli faster, you can also add about 3 tablespoons of water into the skillet and cover with a lid to steam them.
Add the beef into the skillet. Add the sauce mixture into the skillet and let cook until the sauce thickens to the desired consistency. Mix well until the beef and broccolis are all well coated with the sauce.
Cook the noodles separately according to the packaging's instructions. Add the cooked noodles into the skillet and combine to coat the noodle with the sauce. Serve in a bowl.