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. Stir 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.
Skim the surface regularly for 35 to 40 minutes or until the chestnuts can be mashed easily with a fork.
Add the heavy cream and simmer five to 10 minutes more. Then discard the bay leaf and thyme.
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 two 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 three to four days or frozen for up to a month. Bring the soup back to a boil before serving. Best served hot, ladeled into warm bowls.