Place the beef stew meat in the slow cooker. In a small bowl, whisk together the soy sauce, brown sugar, garlic, ginger, and beef broth. Pour the mixture over the beef.
Cover and cook on low for 6 hours until the beef is tender.
In the final 30 minutes of cooking, stir the cornstarch with 2 tablespoons of water to make a slurry. Add it to the slow cooker along with the broccoli florets. Stir gently, then cover again to finish cooking.
Spoon the beef and broccoli mixture over bowls of cooked rice. Sprinkle with sesame seeds before serving.