1. Place potatoes in water to cover. Bring to a boil; cook 16 to 18 minutes or until tender. Drain; cool 15 minutes. Cut into cubes.
2. Combine mayonnaise and next 4 ingredients in a large bowl. Add potato, onions, relish, and eggs; toss to coat. Serve immediately, or cover and chill. Sprinkle with 1/8 teaspoon pepper and parsley, if desired, just before serving.