Boil the potatoes in salted water for approx. 5 mins., drain the water, leave the potatoes to steam for several minutes. Transfer the parboiled potatoes to a baking tray lined with baking paper, drizzle with oil and season with salt and pepper, mix well, spread the potatoes out on the tray.
Roast for 25-30 mins. in the centre of an oven preheated to 190°C, turning the potatoes once during this time.
Place all of the ingredients except the olive oil in a food processor, blend to a smooth sauce. Heat the oil in a frying pan, add the sauce and simmer over a medium heat, stirring until it has reduced slightly.
Pour the hot sauce over the potatoes, garnish with parsley. Serve with the vegan mayonnaise.