Thinly slice the beef chuck roast against the grain into strips about 1/4 inch thick.
In a medium bowl, whisk together beef broth, soy sauce, brown sugar, minced garlic, sesame oil, grated ginger, and crushed red pepper flakes until sugar is dissolved.
Place the sliced beef into the slow cooker and pour the sauce mixture over the beef. Stir to coat evenly.
Cover and cook on low for 4 hours, or until the beef is tender.
About 30 minutes before serving, add the broccoli florets to the slow cooker and stir to combine.
In a small bowl, mix cornstarch and water to create a slurry.
Pour the cornstarch slurry into the slow cooker and stir well. Cover and cook for an additional 30 minutes, or until the sauce has thickened and broccoli is tender-crisp.
Taste and adjust seasoning if needed.
Serve the beef and broccoli over steamed rice or noodles, garnished with sliced green onions and toasted sesame seeds.