Bring a Dutch oven of water to a boil over high heat and add the cubed red potatoes (skin on). Boil for 10–15 minutes, until tender when pierced with a fork, then drain well.

Spread the drained potatoes on a tray or in the pot and cool until no longer steaming. Allow 5–10 minutes at room temperature so the salad dressing won’t thin.

In a bowl, whisk the mayonnaise, Dijon mustard, white wine vinegar, salt, and pepper until smooth and creamy. Taste and adjust with more salt and pepper if needed.

Add the cooled potatoes, diced celery, finely diced red onion, and chopped parsley to a large bowl. Toss gently to distribute the mix evenly.

Pour the dressing over the potato mixture and toss well until every piece is coated. Scrape the bottom of the bowl to avoid dry spots.

Cover and refrigerate for at least 2 hours before serving. Chill until cold and slightly thickened, with a cohesive creamy texture.