Peel and finely chop the shallots, sauté in a little butter. Add the chestnuts and sweat with them. Deglaze with the beef stock and let it simmer until the chestnuts are soft. Top up with sweet cream and crème fraiche. Season to taste with salt, cayenne pepper and a little lemon juice. Mix with a hand blender and strain through a sieve.
Arrange the soup and then refine it with truffle oil or alternatively slice fresh white truffle onto the foamed soup. Serve immediately.