In a medium bowl, whisk together beef broth, soy sauce, brown sugar, sesame oil, garlic, and ginger.
Add sliced beef to the crockpot and pour the sauce over it. Stir to coat evenly.
Cover and cook on LOW for 5–6 hours or HIGH for 3–4 hours, until beef is tender.
Mix cornstarch and water in a small bowl, then stir it into the crockpot 30 minutes before serving to thicken the sauce.
Add broccoli florets during the last 20–30 minutes of cooking; cover again to steam until bright green and tender-crisp.
Serve hot over rice, garnished with sesame seeds and green onions.