Wash and scrub the potatoes thoroughly, then cut them in half if large.
Place potatoes in a large pot and cover with cold water.
Bring the water to a boil and cook until fork-tender, about 15-20 minutes.
Drain the potatoes and let them cool slightly.
While the potatoes are cooling, prepare the dressing by whisking together vinegar, oil, mustard, sugar, salt, and pepper.
Dice the onions finely and add them to the dressing.
Once the potatoes are cool enough to handle, cut them into bite-sized pieces.
Add the warm potatoes to the dressing and gently mix to coat.
Let the salad sit at room temperature for at least 30 minutes to allow flavors to meld.
Garnish with fresh parsley and serve warm or at room temperature.