Place the cubed potatoes in a large pot and cover with cold water. Bring to a boil over high heat, then reduce to a simmer. Cook for 15–20 minutes, or until potatoes are tender when pierced with a fork. Drain and transfer to a large mixing bowl.
While potatoes cook, peel and chop the hard-boiled eggs. Finely dice the celery and red onion. Add the eggs, celery, onion, and parsley to the warm potatoes and gently toss to combine.
In a small bowl, whisk together mayonnaise, Dijon mustard, apple cider vinegar, salt, and black pepper until smooth. Pour the dressing over the potato mixture and stir gently until well coated.
Let the salad cool to room temperature, then refrigerate for at least 1 hour before serving to allow flavors to meld. Stir in chopped chives just before serving if using.
Notes
Serve chilled as a side dish at picnics, barbecues, or family dinners.