1. Rinse shanks, pat dry, and arrange slightly apart in a 10- by 15-inch pan; sprinkle all over with pepper.
2. Bake shanks in a 450° oven until well browned, 20 to 30 minutes.
3. Meanwhile, in a 4 1/2-quart or larger electric slow-cooker, combine onion, bell pepper, celery, artichoke hearts, olives, capers, and basil. Set shanks on vegetables in cooker. Add tomatoes with juice, vinegar, and any lamb juices from baking pan.
4. Cover and cook until lamb is very tender when pierced with a fork, 6 to 6 1/2 hours on low, 4 to 4 1/2 hours on high.
5. With a slotted spoon, transfer each shank to a wide, shallow bowl and keep warm. Skim and discard fat from cooking liquid. Turn cooker to high. In a small bowl, mix cornstarch with 1 1/2 tablespoons water; pour into cooker and stir often until sauce is bubbling, about 10 minutes. Spoon sauce and vegetables over lamb, and sprinkle portions with parsley.