Preheat the oven to 400°F. Coat a 13- x 9-inch baking dish and an 8-inch baking dish with cooking spray.
In a large skillet over medium-high heat, melt butter. Add celery and onions, and sauté for 5 to 6 minutes or until onions are tender. Stir in sage and sauté for an additional 1 minute.
In a large bowl add Cornbread Crumbles.
Add shredded roasted chicken, sliced Andouille sausages, beaten eggs, chicken broth, freshly ground pepper, and the sautéed celery-onion-sage mixture to the bowl. Stir until all the ingredients are well blended.
Divide the cornbread mixture between the lightly greased 13- x 9-inch baking dish and the lightly greased 8-inch square baking dish.
Bake at 400°F for 45 to 55 minutes or until the dressing is set and golden brown.