Layer first 4 ingredients in a 3-quart bowl. Drain artichoke hearts, reserving marinade. Layer artichoke hearts, pepperoni, and onion over zucchini. Cover and chill.
Combine reserved artichoke marinade, mayonnaise, and cheese in a small bowl; cover and chill. Spread mayonnaise mixture over salad just before serving. Sprinkle with chopped parsley.