Place the sliced flank steak in the slow cooker. Add the soy sauce, beef broth, minced garlic, grated ginger, honey, and sesame oil. Stir to coat the beef evenly.
Cover and cook on low for 5 hours until the beef is tender.
In the final hour, stir in the broccoli florets so they stay firm.
Mix the cornstarch with the water to form a slurry. Stir it into the slow cooker and cook on high for 15 minutes until the sauce thickens.
Serve the beef and broccoli over cooked rice. Top with sliced green onions and sesame seeds.