Preheat the oven to 350°F (175°C). Grease a 9x13 inch baking dish with butter or nonstick spray.
In a large bowl, combine the cornbread stuffing mix and melted butter. Slowly add the chicken broth and stir until the dressing is evenly moistened.
Add the shredded chicken, chopped onion, chopped celery, cream of chicken soup and milk to the bowl. Stir until everything is well combined. Season with salt and black pepper.
Transfer the mixture into the prepared baking dish, spreading it into an even layer. Dot the top with a little extra butter if desired.
Bake uncovered in the preheated oven for 40 to 45 minutes, or until the top is golden and the casserole is heated through.
Remove from the oven and let the casserole rest for 10 minutes. Garnish with chopped fresh parsley, serve warm, and enjoy.
Notes
This casserole is great for using leftover roast chicken. For a crispier top, sprinkle with shredded cheddar cheese during the last 10 minutes of baking.