Preheat the oven to 350°F (175°C).
In a skillet, melt butter over medium heat.
Add diced onions and celery; sauté until tender.
In a large bowl, combine crumbled cornbread, sautéed vegetables, and herbs.
Pour in the broth gradually, mixing well until moistened.
Stir in beaten eggs and chopped parsley.
Season with salt and pepper to taste.
Transfer the mixture into a greased baking dish.
Bake for 30 minutes or until golden brown on top.
Let cool slightly before serving.