As soon as potatoes are tender, drain and remove skins; slice into a bowl. While potatoes are still hot, add egg, onion, and parsley and toss lightly. Immediately, our oil mixture over potatoes but do not toss. Let marinate at room temperature for 1 hour. Add mayonnaise and toss lightly. Makes 6 (1-cup) or 8 (3/4-cup) servings.