Whisk soy sauce, oyster sauce, brown sugar, beef broth, rice vinegar, cornstarch, sesame oil, red pepper, and black pepper.
Heat oil in a large skillet over medium-high. Add ground beef and break into crumbles.
Cook beef until browned with crisp edges, about 5–6 minutes. Spoon off excess fat if needed.
Stir in garlic and ginger. Cook until fragrant, about 30 seconds.
Add broccoli and water. Cover and steam until bright green, 2–3 minutes.
Pour in the sauce. Toss and simmer until thick and glossy, 2–3 minutes.
Taste and season with salt if needed. Top with green onions and sesame seeds. Serve hot.