Combine beef broth, soy sauce, brown sugar, sesame oil, and minced garlic in a medium mixing bowl and whisk until smooth.
Place the beef strips into the slow cooker and pour the sauce over them, tossing gently to coat all the meat.
Set the slow cooker to LOW and cook the beef for between 2.5 to 3.5 hours.
About one hour before the cooking time ends, take out 1/4 cup of the cooking liquid and mix it thoroughly with the cornstarch in a small bowl.
Gradually mix this cornstarch slurry back into the slow cooker to thicken the sauce.
Add the frozen broccoli to the slow cooker during the last 30 minutes of cooking, stir to blend it in, then cover and cook until tender. For softer broccoli, add it 45 to 60 minutes before the end.
If you like, garnish the finished dish with sliced green onions and sesame seeds. Serve hot over white rice.