Preheat your oven to 350 degrees F. Grease a 9×13 inch baking dish.
Crumble the prepared cornbread into a large bowl.
In a large skillet over medium heat, melt the butter. Add the celery and onion. Cook until softened, about 8 minutes.
Stir the cooked vegetables, salt, pepper, sage, and thyme into the cornbread crumbs. Mix well.
In a separate bowl, whisk the eggs with 2 cups of the chicken broth.
Pour the egg and broth mixture over the cornbread mixture. Toss gently until everything is just moistened. Add the remaining broth if the mixture seems too dry.
Transfer the dressing mixture to the prepared baking dish.
Bake for 40 to 50 minutes, or until the top is golden brown and the center is set.
Notes
For a richer flavor, use homemade cornbread made without sugar.
If you prefer a crispier top, bake uncovered.
You can prepare the cornbread one day ahead to save time.