In the bowl of a 6-quart slow cooker, combine the beef broth, soy sauce, brown sugar, sesame oil, and minced garlic. Whisk the mixture until fully blended.
Add the sliced beef to the sauce and gently toss to coat. Secure the lid and cook on low heat for 5 hours.
Once the beef has cooked, mix the cornstarch and water in a small bowl to form a smooth slurry. Pour this into the slow cooker, stirring to incorporate.
Scatter the frozen broccoli florets over the beef and sauce. Stir gently to combine. Cover and continue cooking for an additional 30 minutes, allowing the broccoli to cook and the sauce to thicken.
Serve the savory beef and broccoli over warm white rice, if desired. Enjoy your delicious meal!