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Set a large skillet, saute pan, or Dutch oven over medium-high heat. Add the ground beef and cook until no longer pink, breaking apart and stirring as the meat cooks.
While the beef is cooking, combine the beef broth, oyster sauce, soy sauce, honey, rice vinegar, garlic powder, and red pepper flakes in a bowl or large measuring cup; set aside.
After the beef is cooked, push it to the edges of the pan, add the garlic and ginger in the center, and stir for a minute or two until fragrant. Drain the grease from the pan. Add the sauce and the broccoli to the pan; stir to combine. Bring to a boil then reduce to a simmer. Cook for several minutes (using the cooking time on the package of frozen broccoli as a guide) and stir occasionally until the broccoli is cooked to your desired tenderness.
In a small bowl, use a fork to whisk the cornstarch into the water until dissolved. Slowly pour the cornstarch slurry into the pan while stirring the beef and broccoli. Bring to a boil and cook for a minute or two, stirring occasionally, until the sauce is thickened. Stir in the sesame oil, if using, and serve hot over rice or noodles.