In a slow cooker, combine the soy sauce, brown sugar, cornstarch, garlic, ginger, sesame oil, and black pepper. Stir until well mixed.
Add the sliced flank steak to the slow cooker and toss to coat the meat evenly with the sauce.
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 and stir to combine. Cover and continue cooking until the broccoli is tender.
Serve the beef and broccoli over cooked white rice.