Place the potatoes in a saucepan and cover with cold water. Add the salt. Bring to a boil, reduce the heat, and allow the potatoes to simmer until tender, about 10 minutes. Drain
While the potatoes are simmering, in large bowl, mix together the mayonnaise, Dijon mustard, vinegar, salt and pepper. Add the onion, celery, parsley and relish, if using, and stir. Add the drained warm potatoes and toss to coat with the dressing. Cover the salad and wither cool to room temperature or refrigerate for at least 3 hours, or up to 4 days, to cool completely.
Remove from the fridge about 20 minutes before serving to bring the salad to room temperature.