Place the sliced flank steak in the slow cooker. Add the soy sauce, beef broth, brown sugar, minced garlic, and ground ginger. Stir to coat the beef evenly.

Cover and cook on low for 5 hours. The beef should become tender but not fall apart.

In a small bowl, mix the cornstarch with 2 tablespoons of cold water. Stir this slurry into the slow cooker to thicken the sauce. Add the broccoli florets and cook on low for 1 more hour.

While the broccoli finishes, cook the rice. Rinse the rice under cold water, then combine it with 4 cups of water and a pinch of salt in a saucepan. Bring to a boil, reduce heat, cover, and simmer for 18 minutes. Remove from heat and let it rest covered for 5 minutes.

Stir the sesame oil into the beef and broccoli mixture. Taste and adjust with salt and pepper if needed. Serve the beef and broccoli over the steamed rice.