Place the sliced beef into the slow cooker, spreading it evenly.
In a bowl, whisk together beef broth, soy sauce, brown sugar, sesame oil, garlic, and ginger.
Pour the sauce mixture over the beef, making sure all pieces are coated.
Cover and cook on LOW for 4–5 hours or HIGH for 2–3 hours, until the beef is tender.
In a small bowl, mix cornstarch with water to create a slurry.
Stir the slurry into the slow cooker to thicken the sauce.
Add the broccoli florets and gently stir.
Cover and cook for an additional 20–30 minutes until the broccoli is tender but still bright green.
Taste and adjust seasoning with salt and black pepper if needed.
Serve warm.