If you are using fresh (not pre-cooked) chestnuts, wash well and make a slit on the side of each one.
Boil in a deep pot of water for 10-15 minutes.
Take out with a slotted spoon and peel.
Place the chestnut meat (no problem if it's broken in pieces) in the broth and continue boiling until soft. At this time, start toasting your breadcrumbs (which you can prepare ahead of time out of stale bread or use from a jar).
In a large bowl, mash chestnut pieces while still hot with a fork, the way you would potatoes for a puree.
Dice the fatback small (which is easier if you do the cutting with a non-serrated knife immediately after you take the slab out of the fridge and finish the cutting while it's still cold), and add to the mashed chestnuts.
Add the toasted breadcrumbs, the chopped parsley, the lemon zest, the butter softened at room temperature, and the beaten egg. Mix everything well with your hands, as you would ground meat.
Sprinkle generously with salt and pepper to taste and mix again.
* Fatback is a wonderful type of fat with unique qualities, but can be hard to find if you have not made friends with a pig farmer / well-sourced butcher or don't share in community-assisted farming. You could substitute bacon with some measure of success in this recipe, but try to use only the fat (white) part of a non-flavored bacon slab, leaving the red part for your breakfast routine.
Pour the milk in a double-boiler (or use your own version of make-shift double-pot boiling, as I do with a larger and a smaller saucepans nested into each other, with the larger one half-way full of water).
Add the peeled onion head, in which you have stuck the cloves. Sprinkle in the ground nutmeg. Get the liquid heated on medium heat for 30 minutes, without allowing boiling to start. (Close supervision is recommended, as is adjusting the temperature if you see signs of bubbles coming up.)
While stirring constantly, add the cup (=2oz.) of breadcrumbs (here they do not need to be toasted since they will be soaked in milk anyway).
Continuing stirring, add half the butter (1 tablespoon), plus the salt and pepper to taste. Cook for 20 minutes on medium-low heat.
With a fork, remove the onion head (and any stray cloves which might have fallen from it), which you can chop and use in a soup or stew later.
Take off the stove and stir in the heaping tablespoon of cream (if you cannot find proper cooking cream which is not common in the US, you can use something called "european style heavy cream" or even plain sour cream, but remember to place it on the stove near the heat while you are cooking, so that by this point it is at above room temperature in order to avoid curdling) and the remaining one tablespoon of butter. Pour in a gravy boat and serve.