Sweat the onion, potato, and half of the carrots in the butter for a few minutes until just tender, then add the wine and cook off. Don’t let the bottom of the pan darken.
Add the stock, salt and sugar and bring the mixture to a boil, then turn the heat down to low and cook for 20 minutes. Add the watercress and puree with a handblender, leaving it a bit coarse.
Add the remaining shaved carrot and pulse a few times to break it up. There should be visible pieces of carrot and watercress in the soup.
Allow the soup to sit for a few minutes so the carrot particles become tender, or put back on the heat for a moment, then double check the seasoning adjust as needed, and serve with a few sprigs of watercress on top, cracked black pepper, and drizzles of extra virgin olive oil.