In a medium-sized mixing bowl, whisk together the beef stock, soy sauce, brown sugar, sesame oil, minced garlic, and ground ginger until well combined.
Lay the sliced beef chuck roast evenly at the bottom of the slow cooker and pour the sauce over it, tossing to coat.
Cover the slow cooker and cook on HIGH for 3 hours or on LOW for 5-6 hours.
Remove ¼ cup of the cooking liquid and whisk with cornstarch until smooth, then add back to the slow cooker.
Add the broccoli florets, cover, and continue cooking on HIGH for an additional 30 minutes, until the broccoli is tender.
Serve hot over cooked white rice, garnished with toasted sesame seeds and sliced green onions.
Notes
For a lighter version, substitute chicken breast for the beef. Add extra vegetables for more nutrition.