First, put a saucepan of water on a high heat and add in a good pinch of salt. Bring the water up to the boil, then add in the new potatoes. Boil for them 15-20 minutes until they are tender. While the potatoes are cooking, make the dressing.
Mix together the walnut oil or the extra-virgin olive oil, whichever you're using, the sherry vinegar, the Dijon mustard, and some salt and freshly ground black pepper to season. Once the potatoes are cooked, cut them in half or quarters while they are still hot and drizzle some of the dressing over the top and set them aside.