Place the sliced flank steak into the slow cooker.
In a bowl, stir together the soy sauce, brown sugar, minced garlic, grated ginger, and sesame oil until the sugar dissolves.
Pour the sauce over the beef and stir to coat. Cover and cook on low for 5 hours.
In the last 45 minutes, add the broccoli florets.
Mix the cornstarch with 2 tablespoons of water to make a slurry, then stir it into the slow cooker to thicken the sauce.
Cook for the remaining time until the broccoli is tender and the sauce has thickened.
Spoon the beef and broccoli over the cooked rice. Top each bowl with sliced green onions and sesame seeds.