Preheat your oven to 375.
Crumble the cornbread into a very large mixing bowl. It's helpful to do this. 1-2 days ahead, so your cornbread is just ever so slightly dryer.
In a separate pan, melt the butter in a skillet over medium heat. Add the onion, celery, and carrots. Cook until the vegetables are soft and fragrant.
Add the sautéed vegetables to the cornbread.
Stir in the shredded chicken, turkey gravy mix, heavy cream, and enough chicken broth to create a moist but not runny mixture.
Add the sage, garlic and poultry seasonings, salt, and pepper. Do not be shy with the sage. The flavor mellows and becomes warm and comforting as it bakes.
Pour mixture over your crumbled cornbread mixture. It helps to do this in 1-2 batches, to avoid spilling.
Right before baking, mix in the beaten egg. This helps the dressing hold together without becoming dense. If you want to taste to make sure you have enough sage, salt and pepper, be sure to do that before adding the egg.
Transfer the mixture to a greased baking dish. Cover tightly with foil.
Bake at 375 for 50 minutes. Remove the foil for the last few minutes if you prefer a more golden top. A toothpick should come out of the middle clean to be sure that it's done.
Let it rest for a few minutes before serving so everything sets.