Make the sauce. In a bowl, whisk soy sauce, oyster sauce, hoisin, honey, rice vinegar, sesame oil, red pepper flakes, broth, and cornstarch until smooth. Set aside.
Prep the broccoli. If using fresh, cut into small, uniform florets.
If using frozen, do not thaw; just break up any clumps.
Brown the beef. Heat 1 tablespoon oil in a large skillet or wok over medium-high heat. Add ground beef and break it up. Cook until browned with crispy bits, 5–7 minutes.
Season lightly with salt and pepper. Transfer to a plate, leaving some fat in the pan.
Sauté aromatics. Add remaining 1 tablespoon oil if needed. Add onion and cook 2 minutes until slightly softened.
Stir in garlic and ginger and cook 30–45 seconds until fragrant.
Cook the broccoli. Add florets to the pan with a pinch of salt. Stir-fry 2–3 minutes, then splash in 2–3 tablespoons water and cover for 2 minutes to steam until crisp-tender. Uncover and let excess moisture cook off.
Combine and sauce. Return beef to the pan.
Whisk the sauce again (cornstarch settles) and pour it in. Toss everything to coat. Cook 2–3 minutes, stirring, until the sauce thickens and turns glossy.
Finish and serve. Taste and adjust: add more vinegar for brightness, honey for sweetness, or chili for heat.
Top with green onions and sesame seeds. Serve hot over rice or noodles, with lime wedges if you like.