Rinse the shanks, pat dry, and arrange slightly apart in a 10x15-inch pan; sprinkle all over with pepper.
Bake the shanks until well-browned, 20 to 30 minutes.
Meanwhile, in a 4.5-quart or larger electric slow cooker, combine the onion, bell pepper, celery, artichoke hearts, olives, capers and basil. Set the shanks on the vegetables in the cooker. Add the tomatoes with juice, vinegar, and any lamb juices from the baking pan.
Cover and cook until the lamb is very tender when pierced with a fork, 6 to 6½ hours on low, 4 to 4½ hours on high.
With a slotted spoon, transfer each shank to a wide, shallow bowl and keep warm. Skim and discard the fat from the cooking liquid. Turn the cooker to high. In a small bowl, mix the cornstarch with 1½ tablespoons water; pour into the cooker and stir often until the sauce is bubbling, about 10 minutes. Spoon the sauce and vegetables over the lamb, and sprinkle individual portions with parsley.