Place the sliced beef at the bottom of your crockpot.
In a bowl, combine the beef broth, soy sauce, brown sugar, sesame oil, and minced garlic and mix well.
Pour the sauce mixture evenly over the beef in the crockpot.
Set the crockpot to low and let the beef cook for 3 to 4 hours until it becomes tender.
Carefully remove about ¼ cup of the cooking liquid and whisk in the cornstarch until smooth.
Stir this cornstarch mixture back into the crockpot and add the broccoli on top.
Increase the heat to high and cook for another 20 minutes or until the broccoli reaches your desired tenderness.
Give everything a good stir and season to taste if desired.
Serve the beef and broccoli hot over cooked rice and sprinkle with sesame seeds to finish.