Place the beef stew meat in the slow cooker. Add the beef broth, soy sauce, brown sugar, and minced garlic. Stir to combine the sauce ingredients with the meat.
Cover and cook on low for 6 hours. The beef should become tender during this time.
In a small bowl, mix the cornstarch with 2 tablespoons of the cooking liquid from the slow cooker until smooth. Stir this mixture back into the pot.
Add the frozen broccoli florets. Cover and cook on high for 30 minutes, or until the broccoli is tender but still bright.
Serve the beef and broccoli over cooked rice. Sprinkle sesame seeds on top before eating.