Preheat oven to 375 degrees F.
In a large skillet, melt 1/2 cup butter over medium heat. Add onion, carrots and celery. Cook and stir 8 minutes, or until softened.
In a large bowl, mix vegetable mixture, cornbread, biscuits, chicken broth, eggs, milk, sage, celery leaves, salt and pepper. Mixture will be soupy.
Transfer mixture to a 3-quart baking dish. Cut remaining 1/4 cup butter into cubes and scatter over dressing.
Bake 45 minutes or until browned and 165 degrees F.