Bring a large pot of salted water to a boil, then carefully add the potatoes. Cook until they are just tender when pierced with a fork, about 12-15 minutes.
Drain the potatoes and immediately transfer them to an ice bath to stop the cooking and help them cool quickly. Let them sit for about 10 minutes until completely chilled.
Peel the potatoes if desired, then cut them into uniform, bite-sized cubes while they are still slightly warm—this helps them absorb the dressing better.
In a large mixing bowl, whisk together the mayonnaise, Dijon mustard, and apple cider vinegar until smooth and well combined.
Add the diced potatoes to the bowl with the dressing, gently folding to coat each piece without breaking them apart.
Stir in the finely diced red onion and chopped celery, mixing gently to distribute evenly.
Season the salad with salt and freshly ground black pepper, tasting and adjusting the seasoning as needed.
Chop fresh chives or dill and fold them into the salad just before serving to keep their bright aroma and flavor intact.
Cover the bowl and refrigerate for at least one hour before serving to allow flavors to meld and the salad to chill thoroughly.
Serve the potato salad chilled or at room temperature, enjoying the satisfying crunch of the cooled potatoes combined with the creamy, tangy dressing.
