Heat a large skillet over medium heat. Add the ground beef and diced onion and cook, breaking the beef into pieces, until the meat is browned and the onion is softened, about 5–7 minutes.
Stir in the sesame oil, then add the chopped broccoli florets and cook for 1–2 minutes until they begin to brighten and soften.
Add the soy sauce, hoisin sauce, minced garlic, minced ginger, and brown sugar if using; stir to coat everything evenly.
Let the mixture simmer for 2–3 minutes more, stirring occasionally, until the broccoli is tender and the sauce is slightly reduced.
Serve the beef and broccoli warm over rice, in lettuce wraps, or in bowls.
