Freeze steak ~20-30 mins for easier thin slicing, then slice against grain.
Whisk sauce ingredients (oyster/hoisin, soy, sugar, broth, cornstarch) until smooth.
Heat oil in large skillet/wok over medium-high. Add broccoli, maybe a splash water and cover for ~3-5 mins until crisp-tender. Remove broccoli.
Increase heat to high. Add beef in single layer, sear ~2–3 mins until browned, remove.
In same pan, add garlic & ginger ~30 seconds, then return beef + broccoli, pour in sauce, stir until sauce thickens (~1–2 mins).
Add sesame oil, adjust salt/pepper. Serve immediately over rice/noodles.