Place the beef into the bottom of the slow cooker.
In a medium mixing bowl, whisk together the beef broth, low-sodium soy sauce, brown sugar, sesame oil, minced garlic, and grated ginger until thoroughly combined.
Pour the sauce mixture over the beef. Gently stir until all of the sliced beef is coated in the sauce.
Cover the slow cooker and cook on LOW for about 4 hours, or until the beef is tender. Alternatively, cook on HIGH for approximately 2–3 hours.
During the final 45–60 minutes of cooking, whisk together the cornstarch and cold water in a small bowl until completely smooth and no lumps remain.
Pour the cornstarch slurry into the slow cooker and stir well to incorporate it into the sauce.
Add the fresh broccoli florets and gently stir them into the beef and sauce.
Cover and continue cooking on LOW for 45–60 minutes, or until the sauce has thickened and the broccoli has reached your desired tenderness. For firmer, crisp-tender broccoli, begin checking after about 30 minutes.
Give the beef and broccoli a final stir. Serve immediately over warm white rice and garnish with sesame seeds and sliced green onions, if desired.