Cook chestnuts or, best of all, use fully cooked chestnuts.
Cut the sweet potato into small pieces. Chop the onion and chilli and fry them. Add the sweet potato and roast it too. Add chestnuts and deglaze with the wine. Stir the stock and cream into the saucepan until everything is well covered. The chestnuts and sweet potatoes make a thick soup, so you can use a little more liquid. Season with fresh rosemary and thyme. If you use dried spices, you should roast them beforehand. Let the soup simmer in a closed pot for about 20 - 30 minutes.
When the sweet potatoes are done, puree them with the blender. If the soup is too thick, add a little broth and season with salt if necessary.