Dice onion into small dice and add the oil, vinegar, sugar then set aside.
Place whole unpeeled potatoes into cold salted water to cover. Set over high heat, bring to a boil, and cook until fork tender. Remove from water and allow potatoes to cool.
Add mayonnaise to the warm potatoes to moisten not soak.
Add onion/oil mixture, the chopped parsley, salt, & pepper mix well.
Check that the mixture is wet but not runny, adding more mayo if needed.
Salad will taste best if done the day before serving.