Boil the potatoes in a pot of salted water until just tender. Alternatively, steam the potatoes using a steamer. Drain and let cool slightly.
Whisk together the vinegar, mustard and garlic. While still whisking, add the oil until emulsified. Season with salt and pepper.
Fire up your grill for medium-high cooking.
Toss the potatoes with a little oil. Season with salt and pepper and add to a grill basket. Note: I put the grill basket over a sheet pan so that any excess oil drips off.
Place the basket onto the grill and cook for 5-10 minutes, stirring gently, or until the potatoes are done and have a light char.
Transfer potatoes to a large bowl and drizzle with the dressing. Toss to coat.
Serve garnished with the chopped parsley.