Place the potato cubes in a large pot and cover with cold water. Bring to a boil over high heat, then reduce to a simmer and cook for 10-12 minutes until tender but not mushy.
While the potatoes cook, whisk together olive oil, white wine vinegar, Dijon mustard, salt, pepper, and sugar in a small bowl to make the dressing.
Drain the cooked potatoes and let them cool slightly in a large mixing bowl for about 5 minutes.
Add the red onion, celery, and parsley to the potatoes. Pour the dressing over the top and gently toss to combine everything evenly.
Let the salad rest at room temperature for 10 minutes to allow flavors to meld, then serve immediately or chill briefly before enjoying.
