In a medium bowl, mix together beef broth, soy sauce, dark brown sugar, sesame oil, and minced garlic until the sauce is well blended.
Place the sliced beef evenly in the slow cooker, then pour the sauce over the meat, tossing gently to coat all pieces.
Set the slow cooker to low heat and cook the beef for 2.5 to 3.5 hours until tender.
One hour before cooking ends, take out 1/4 cup of the cooking liquid and whisk it with cornstarch in a small bowl to create a slurry.
Slowly stir the cornstarch mixture back into the slow cooker to thicken the sauce.
Add the frozen broccoli to the slow cooker during the last 30 minutes of cooking, mixing to combine, covering, and letting it cook until the broccoli is heated through and tender. For softer broccoli, add it with 45 to 60 minutes remaining.
Optional: Garnish with sliced green onions and sesame seeds before serving. Serve this tasty dish warm over white rice.