Prepare the beef by trimming any excess fat from the beef chuck roast and slicing it thinly against the grain into bite-sized strips.
Place the sliced beef evenly in the bottom of the slow cooker, spreading it out so the pieces are not clumped together.
In a medium bowl, whisk together the low-sodium beef broth, low-sodium soy sauce, packed brown sugar, oyster sauce, rice vinegar, sesame oil, minced garlic, finely grated fresh ginger, black pepper, and crushed red pepper flakes (if using) until the brown sugar is dissolved and the mixture is smooth.
Pour the prepared sauce mixture over the sliced beef in the slow cooker, gently stirring to coat all of the beef pieces in the sauce.
Cover the slow cooker with the lid and cook the beef mixture on low heat for 3.5 hours, or until the beef is very tender but still holding its shape.
About 20 minutes before the beef is finished, whisk together the cornstarch and cold water in a small bowl to form a smooth slurry with no lumps.
Uncover the slow cooker, pour the cornstarch slurry into the beef and sauce, and stir well to combine, making sure the slurry is evenly distributed.
Add the fresh broccoli florets directly on top of the beef and sauce in the slow cooker, gently pressing them down so they are lightly coated.
Cover the slow cooker again and continue cooking on high heat for 20 to 25 minutes, or until the sauce has thickened and the broccoli is crisp-tender.
While the broccoli beef finishes cooking, prepare the cooked white rice according to package instructions if it is not already made, and keep it warm for serving.
Once the broccoli is crisp-tender and the sauce is glossy and thick, taste the sauce and adjust the seasoning if desired, then turn off the slow cooker.
Spoon the broccoli beef over bowls of cooked white rice, making sure to include plenty of sauce with each serving.
Garnish each serving with sliced green onions and a light sprinkle of toasted sesame seeds just before serving.