Turn slow cooker on low and allow it to begin warming. Add beef broth, soy sauce, fish sauce, honey, sesame oil, and garlic directly to the slow cooker. Whisk until the honey is completely incorporated. The warm slow cooker will make this very easy.
Add cubed chuck roast directly to sauce. Stir to combine. Cover and cook on low for 6 hours. (The longer you cook your meat the more it will fall apart. Adjust your cooking time to your preference for tenderness.)
In a measuring cup combine warm water with cornstarch until the cornstarch is dissolved. Pour directly into the slow cooker, stir to incorporate. Also add broccoli florets (I just use my kitchen shears to trim my heads into florets over the pot because I am lazy and hate washing dishes). Mix well and recover slow cooker.
Cook for an additional 30 minutes. Then serve over brown rice.