Cook celery and onion in butter in a large skillet over medium heat until tender, stirring occasionally. Add kale, and cook, stirring constantly, 3 minutes or until kale wilts. Remove from heat.
Coarsely crumble Cornbread into a large bowl. Add kale mixture; stir well. Add toasted breadcrumbs and next 6 ingredients. Stir in enough broth to moisten dry ingredients as desired. (For moist dressing, add the entire 3 cups broth.)
Spoon dressing into a greased 13" x 9" x 2" pan. Bake, uncovered, at 325° for 1 hour or until top begins to brown.