Add the sliced flank steak to the slow cooker.
In a mixing bowl, whisk the soy sauce, brown sugar, garlic, ginger, and beef broth until the sugar dissolves. Pour the mixture over the beef.
Cover and cook until the beef is tender. Stir the cornstarch into 2 tablespoons of the cooking liquid, then add it back into the slow cooker and stir to thicken the sauce.
Add the broccoli florets during the final portion of cooking so they stay bright and slightly crisp.
Spoon the beef and broccoli over cooked rice. Top each bowl with sliced green onions and sesame seeds.