Grease a baking dish with a little butter (this makes serving easier as it prevents the casserole from sticking to the dish)
In a bowl, whisk the chicken broth and soup together and set this aside
Place the dry stuffing mix, shredded chicken and carrot, onion, and broccoli into a bowl and mix, before placing into the greased dish.
Pour the broth and soup mixture over the mixture in the baking dish (try to evenly disperse the liquid as best you can)
Cover the dish with foil and bake for 30 minutes.
Remove from the oven after 30 minutes, gently mix the casserole before sprinkling over the shredded cheese and bake, uncovered, for another 15 minutes.