Preheat your oven to 350°F (175°C).
In a skillet, melt the butter over medium heat.
Add the chopped onions and celery to the skillet.
Sauté the vegetables until they are soft and translucent, about 5-7 minutes.
In a large mixing bowl, combine the crumbled cornbread, sautéed vegetables, and herbs.
In a separate bowl, whisk together the broth and beaten eggs.
Pour the broth mixture over the cornbread mixture.
Stir gently until everything is well combined and moistened.
Transfer the mixture to a greased baking dish.
Bake for 30-35 minutes, or until the top is golden brown and crispy.