Gather the ingredients.
In a large saucepan, cover the potatoes with cold water and season the water with salt. Bring to a boil over high heat and cook the potatoes until tender, about 15 minutes. Drain and let stand until cool enough to handle, about 10 minutes.
Meanwhile, in a large bowl, whisk the mayonnaise with the mustard and vinegar; season with salt and pepper to taste. Stir in the scallions, parsley, and celery.
Halve the potatoes crosswise and fold them into the dressing. Serve warm or at room temperature.
