Preheat oven to 400°F (200°C). Grease a 9x13 inch baking pan.
In a large bowl, whisk together cornbread mix, eggs, buttermilk, and melted butter until just combined.
Pour batter into the prepared baking pan and bake for 20-25 minutes, or until a toothpick inserted into the center comes out clean. Let cool completely.
Prepare the Dressing
Crumble the cooled cornbread into a very large bowl.
In a large skillet, melt 1 cup of butter over medium heat. Add chopped onion and celery and cook until softened, about 8-10 minutes.
Stir in the cooked onion and celery, parsley, sage, thyme, salt, and pepper into the bowl with the cornbread crumbs.
Pour in the chicken broth and mix gently until everything is moistened.
Transfer the mixture to a greased 9x13 inch baking dish.
Bake in a preheated oven at 350°F (175°C) for 30-40 minutes, or until heated through and lightly browned on top.
Notes
This dressing can be made ahead of time. Cover and refrigerate after assembling. Add a little extra broth before baking if it seems dry.