Step 1

Place potatoes in a large pot; add cold water just to cover; season with salt. Bring to a boil; cook until tender, 30–45 minutes. Drain potatoes; let cool for 30 minutes.

Step 2

Meanwhile, whisk mayonnaise, parsley, relish, Dijon mustard, and vinegar in a small bowl. Season dressing with salt and pepper.

Step 3

Using a spoon or butter knife, peel potatoes; cut into 1/2-inch cubes. Place potatoes in a large bowl. Season with salt and pepper; toss to coat. Add dressing just to coat; stir gently to blend. DO AHEAD: Potato salad can be made 1 day ahead. Cover and chill salad and any remaining dressing separately. Add more dressing to salad before serving, if desired.