Preheat the oven to 350°F (175°C).
Crumble the cornbread into a large mixing bowl and set aside.
Over medium heat melt the butter in a skillet. Add the celery, onion, bell pepper, and garlic. About 7-7 minutes sauté vegetables until tender.
Pour the sautéed vegetables over the crumbled cornbread.
Add the chicken or vegetable broth, dried sage, dried thyme, salt, and black pepper to the bowl. Stir until well combined and the cornbread absorbs the liquid.
Put the mixture in a greased baking dish and spread it evenly.
Bake in the preheated oven for 40-45 minutes, or until the dressing is golden brown and set in the center.
Once the baking is complete remove it from the oven and allow it to cool for a few minutes before serving.