In a large skillet, cook sausage until brown. Drain; set aside.
In the same skillet, melt butter over medium heat. Add onion and celery. Cook over medium heat in hot butter until tender; set aside.
In a large bowl, combine cornbread, cooked sausage, onion mixture, cheese, salt and black pepper. In a small bowl, combine chicken broth and eggs. Drizzle cornbread mixture with broth mixture to moisten.
Spread stuffing evenly in a 2-quart square baking dish. Bake, covered, in a 350 degree F oven for 30 minutes. Uncover and bake 5 to 10 minutes more or until heated through. Makes 4 servings.