Add potatoes to pot and cover with 1 ½ quarts coldwater. Add 2 tablespoons white wine vinegar and 2 tablespoons salt. Bring to a boil and simmer until potatoes are fork tender, about 10-15 minutes. Drain potatoes and set aside to cool slightly.
While potatoes are cooking, in a bowl, combine the oil, lemon juice and mustard; whisk to combine. Add the shallot, capers, parsley, sugar and salt; stir to combine.
Cut potatoes in half, then add to the dressing and stir gently to combine.
Adding vinegar while boiling potatoes will not only flavor the potatoes, but also helps the purple potatoes retain their color!