Slice the beef. Cut the beef into thin strips against the grain.
This helps it stay tender after slow cooking. If using chuck roast, trim excess fat.
Make the sauce. In a bowl, whisk together beef broth, soy sauce, brown sugar, garlic, ginger, sesame oil, and red pepper flakes if using.
Dump and go. Add the beef to the crockpot. Pour the sauce over the top and stir to coat.
Cover with the lid.
Cook low and slow. Cook on Low for 4–5 hours or High for 2–3 hours, until the beef is tender but not shredding apart.
Thicken the sauce. In a small bowl, mix cornstarch with water to make a slurry. Stir it into the crockpot. Cook for 10–15 minutes on High to thicken.
Add broccoli. Stir in the broccoli florets.
Cook for another 15–20 minutes until the broccoli is crisp-tender. If using frozen broccoli, add it straight from the freezer and cook a bit longer.
Taste and adjust. Check seasoning. Add a splash of soy sauce for salt, more brown sugar for sweetness, or a dash of red pepper flakes for heat.
Serve. Spoon over warm rice or noodles.
Garnish with sesame seeds and green onions if you like.