Place potatoes in a saucepan with enough water to cover. Bring to the boil, then cook for 5 to 10 minutes, until tender. Drain, and transfer to a large bowl.
Add the onion, red peppers, olives and artichokes to the bowl with the potatoes. In a separate bowl, whisk together the balsamic vinegar, olive oil, oregano, basil, mustard powder and parsley. Pour over the vegetables, and stir to coat. Chill for at least 4 hours or overnight before serving.