Preheat the oven to 425°F (218°C) and line a heavy-duty rimmed baking sheet with parchment paper.
In a large bowl, toss the cubed potatoes with olive oil, salt, and pepper until thoroughly coated.
Spread the potatoes in a single layer on the prepared baking sheet, ensuring space between pieces to promote browning.
Roast for 30 to 35 minutes, turning with a spatula at the 20-minute mark, until the edges are golden brown and crisp.
In a large mixing bowl, whisk together the mayonnaise, Dijon mustard, and apple cider vinegar.
Fold the minced red onion, celery, parsley, and chives into the dressing mixture.
Remove potatoes from the oven and let cool for approximately 5 minutes on the tray to allow the structure to set while remaining warm.
Gently fold the warm, crispy potatoes into the dressing mixture until evenly coated.
Serve immediately to maintain the contrast between the crispy potato exterior and the creamy dressing.