Spread biscuit and cornbread crumbs in an ungreased pan. Bake at 300° for 15 minutes or until crumbs are toasted, stirring twice.
Sauté celery and onion in butter in a large skillet over medium-high heat until tender. Remove from heat. Combine sauteed mixture, toasted crumbs, parsley, and next 3 ingredients. Stir in broth and milk. Spoon dressing into a greased 13â€� x 9â€� pan. Bake, uncovered, at 350° for 1 hour or until browned.
Shortcut Solution: Six frozen biscuits, baked, or six fast-food biscuits will give you 4 cups crumbs. We tested with Pillsbury frozen biscuits and Pioneer cornbread mix. You could also use frozen baked cornbread and warm it in the microwave oven before crumbling. Or buy cornbread from a cafeteria or deli.
Make Ahead: Spoon prepared dressing into pan; cover and chill overnight. Bake, uncovered, at 350° for 1 hour. Let stand at room temperature until almost serving time. Just before serving, reheat at 350° for 10 to 12 minutes.