We tend to have this in Advent, and then mostly on Wednesdays, because Filia Tertia likes to eat soup after skating. This version is completely vegan and free of oil (not counting the minute amount that may be in stock cubes), but still filling and satisfying.
It's very versatile: you can have fresh or tinned chestnuts, ready-made or home-made puree, use stock from a cube or from veggy scraps (I have a jar of porcini stock paste that's eminently suitable for it), put in leftover mashed potato, leftover potatoes mashed for the purpose, or boil a few potatoes specially, and adjust the spices to your own taste. As always: do not skimp on the spices!
I can imagine making a very non-fasting version for Christmas: fry the onions in goose fat, use beef or poultry stock, make it a bit thinner, and finish it with a dash of madeira or sherry! Cream would probably be over the top: it's very rich already.
Mince the onion as small as you can short of actually grating it. Put it in a thick-bottomed pan and barely cover with a bit of the stock. Add sugar and spices and cook on medium heat until the mixture is almost dry and slightly caramelised.
Add the chestnut puree, the potato and some more of the stock; stir forcefully until it's smooth. Add the rest of the stock and finally the whole chestnuts. Taste it and add some salt if needed (some stock cubes can be very salty).
Serve with crusty bread and put the pepper mill on the table.