In a bowl, whisk together soy sauce, brown sugar, cornstarch, minced garlic, minced ginger, sesame oil, beef broth, and red pepper flakes (if using).
Place the sliced flank steak in the slow cooker and pour the sauce mixture over the meat. Stir to coat the beef evenly.
Cover and cook on low for 4-5 hours or on high for 2-3 hours, until the beef is tender.
About 30 minutes before serving, add the broccoli florets to the slow cooker, stirring to combine with the beef and sauce.
Once cooked, serve the beef and broccoli over cooked white rice.