Add the sliced beef, diced onion, garlic, beef broth, soy sauce, brown sugar, and ginger to the slow cooker. Stir gently to combine.
Cover and cook on low for 5–6 hours, until the beef is tender.
In a small bowl, mix the cornstarch with 2 tablespoons of cold water to form a slurry. Stir the slurry into the slow cooker to thicken the sauce.
Add the broccoli florets during the final 30 minutes of cooking. Stir to coat the broccoli florets in the sauce. Cover and continue cooking until the broccoli is tender but still vibrant.
Serve hot over rice or noodles and top with sesame seeds, if desired.