Clean, stuff, and truss six pigeons, place upright in a stewpan, and add one quart boiling water in which celery has been cooked. Cover, and cook slowly three hours or until tender; or cook in oven in a covered earthen dish. Remove from water, cool slightly, sprinkle with salt and pepper, dredge with flour, and brown entire surface in pork fat. Make a sauce with one-fourth cup each butter and flour cooked together and stock remaining in pan; there should be two cups. Place each bird on a slice of dry toast, and pour gravy over all. Garnish with parsley.