Sauté mushrooms, giblets, celery, onion, and parsley in butter in a large skillet until vegetables are tender and giblets are lightly browned.
Combine cornbread crumbs, basil, salt, paprika, and nutmeg in a large mixing bowl; stir well. Add chicken broth and sautéed mixture, stirring well.
Spoon dressing into a lightly greased 12- x 8- x 2-inch baking dish. Bake, uncovered, at 325° for 30 minutes or until thoroughly heated. Serve immediately.
Note: Recipe may be doubled, if necessary, to serve more people.