Start by making the sauce. In a medium bowl, whisk together 1 cup of low-sodium beef broth, ½ cup of low-sodium soy sauce, ⅓ cup of dark brown sugar, 1 tablespoon of sesame oil, and 3 teaspoons of minced garlic.
Next, place the 1 ½ pounds of boneless beef chuck roast strips in your slow cooker. Pour the sauce over the meat, tossing it gently to ensure every piece is coated.
Cover and set your slow cooker to LOW, allowing it to cook for 2.5 to 3.5 hours until fork-tender.
About one hour before the cooking time is up, remove ¼ cup of the cooking sauce and whisk it with 2 tablespoons of cornstarch in a small bowl until smooth. Slowly stir this mixture back into the slow cooker to thicken the sauce.
In the final 30 minutes of cooking, add the 1 (12-ounce) bag of frozen broccoli florets to the slow cooker. Gently stir to incorporate the broccoli into the sauce and meat.
Once everything is cooked, garnish with chopped green onions and sesame seeds if desired. Serve over rice or noodles.