Cut the chuck roast into roughly 1-inch cubes.
In a slow cooker, whisk together the low-sodium soy sauce, brown sugar, beef broth, sesame oil, minced garlic, and minced ginger.
Add the cubed beef to the slow cooker and stir to coat in the sauce.
Cover and cook on low for 6-8 hours, or on high for 3-4 hours, until beef is very tender.
About 30 minutes before beef is done, whisk together cornstarch and cold water in a small bowl until smooth to make a slurry.
Pour the cornstarch slurry into the slow cooker and stir well.
Add broccoli florets to the slow cooker and stir gently to coat.
Cover and continue cooking for 30 minutes, or until broccoli is tender-crisp.
Serve over rice, quinoa, or your choice of side. Garnish with sesame seeds and green onions if desired.