Preheat your oven to 350°F (175°C) and liberally grease a 9x13 inch baking dish.
In a large mixing bowl, combine the shredded chicken, crumbled cornbread, chopped onion, celery, chopped hard-boiled eggs, 2 cups of chicken broth, cream soup, and seasonings (salt, pepper, poultry seasoning). Mix gently until well combined and the cornbread is moistened.
Pour the mixture into the prepared baking dish, spreading it out evenly.
Bake for 40 to 50 minutes, or until the top is golden brown and the center is set.
While the casserole bakes, prepare the gravy. In a saucepan over medium heat, melt 1/2 cup of butter.
Whisk in 1/2 cup of flour and cook for 1-2 minutes to form a roux, stirring constantly.
Gradually whisk in the 1 quart of chicken stock and the heavy cream. Continue to cook and stir until the gravy thickens to your desired consistency.
Slice the warm casserole and serve immediately with the hot gravy poured over the top.