Place potatoes in a saucepan. Cover with water to 2 inches above potatoes; bring to a boil. Reduce heat, and simmer 20 minutes or until tender. Drain. Cool. Peel and cut potatoes into 1-inch cubes. Place potatoes in a large bowl.
Combine mayonnaise and the next 5 ingredients (through tarragon). Add mayonnaise mixture to potatoes; toss gently to coat. Stir in onion and parsley. Cover and chill 1 hour.