In a bowl, whisk together the soy sauce, brown sugar, cornstarch, garlic, ginger, beef broth, sesame oil, and red pepper flakes until smooth.
Place the sliced flank steak in the slow cooker and pour the sauce over the meat, stirring to coat evenly.
Cover and cook on low for 4 hours or on high for 2 hours.
After cooking, add the broccoli florets to the slow cooker, stir, and cover again. Cook on high for an additional 30 minutes, or until the broccoli is tender.
Serve the beef and broccoli over cooked rice, drizzling any extra sauce from the slow cooker over the top.