Sauté celery, onion, green pepper, and parsley in shortening in a skillet over low heat until vegetables are tender.
Combine sautéed vegetables, meat, soft breadcrumbs, eggs, milk, salt, and pepper; mix well. Pack half of meat mixture into a 10- x 6- x 2-inch baking dish. Place egg slices on top of mixture. Spoon remaining meat mixture over egg slices; press lightly on sides to seal. Sprinkle dry breadcrumbs and paprika over top. Bake at 350° for 1 1/2 hours. Loaf maybe served hot or cold.