Drain marinated artichoke hearts and set aside, reserving marinade.
In a small bowl whisk olive oil, vinegar, and reserved marinade.
Alternately layer basil leaves, tomatoes, cheese, and artichoke hearts on platter. Rewhisk marinade and drizzle to taste over entire platter (use any remaining marinade as salad dressing).
Serve immediately. Alternatively, salad can be composed on 6 small individual plates.