Place the cubed beef in your slow cooker.
In a separate bowl, whisk together the soy sauce, beef broth, brown sugar, sesame oil, minced garlic, and minced ginger.
Pour the sauce over the beef in the slow cooker. Stir to ensure the beef is evenly coated.
Cover and cook on low for 6-8 hours, or on high for 3-4 hours, or until the beef is very tender.
About 30 minutes before the end of the cooking time, whisk together the cornstarch and cold water in a small bowl until smooth.
Pour the cornstarch slurry into the slow cooker and stir well to combine.
If using fresh broccoli and you like it more on the crisp side, add the florets to the top after the sauce is thick and the beef has cooked. Cover and let cook for 10-15 more minutes.
Add the frozen broccoli florets to the top after the sauce is thick and the beef has cooked. Stir and cover. Allow it to cook for 15-20 minutes, until heated through.
If using fresh broccoli and want it more well-done add to the beef and sauce for the last 30-45 minutes of cooking time.
Stir everything together, and serve over rice, noodles, or quinoa. Garnish with sesame seeds and sliced green onions, if desired.