In a mixing bowl, whisk together the beef stock, soy sauce, brown sugar and minced garlic.
Add the beef to the slow cooker and pour the liquid over the top, tossing the beef to coat.
Set the slow cooker to cook f or 4 hours on LOW heat.
When the meat is tender, remove a 1/4 cup of the sauce and put in into a small bowl. Add the cornstarch and whisk with a fork to combine. Return the slurry to the slow cooker and stir into the sauce.
Add the broccoli florets to the slow cooker and cover. Cook for another 30 minutes on low so the sauce will thicken and the broccoli will cook.
Season with salt and pepper as desired and serve over white or brown rice.