1) Heat the oil in a stockpot or large casserole over medium heat. Add the onion, leek, apples, celery root, bay leaf, thyme, nutmeg, salt and pepper and cook, stirring occasionally, for about 10 minutes, or until the onions and leeks are soft but not colored. Add the chestnuts and chicken stock and bring to the boil. Lower the heat to a simmer and cook, skimming the surface regularly, 35 to 40 minutes, or until the chestnuts can be mashed easily with a fork. Add the heavy cream and simmer 5 to 10 minutes more, then discard the bay leaf and thyme.
2) Purée the soup until smooth using a blender, food processor or hand-held immersion blender, then pass it through a fine-mesh strainer. At this point, you should have about 2 quarts of soup. If you have more, or if you think the soup is too thin – the soup should have the consistency of a velouté or light cream soup – simmer it over medium heat until thickened. Taste and, if necessary, adjust the seasoning. (The soup can be cooled completely and stored in a covered jar in the refrigerator for 3 to 4 days or frozen for up to a month. Bring the soup back to a boil before serving.)
3) Place a few chestnuts in a pan and let cook on a medium heat. Add some soup (about 2 tablespoons) and let the mixture cook with the chestnuts (about 5 minutes). Top the soup with the chestnuts and serve hot