Wash the chestnuts and boil them in a saucepan with plenty of water (they must be completely covered) and a pinch of salt, for at least 1 hour. Then strain them and, before they cool down too much – in this way it’s easier to remove the thin inner skin – peel them. Rinse the saucepan used to boil them, put the chestnuts back into it, pour in the milk and cook for another 20-30 minutes; stirring from time to time, and trying to squash the chestnuts with the tip of a fork or wooden spoon. When the mixture begins to thicken, add the sugar and vanilla. Stir until the chestnuts are almost a purée. Push the mixture through a potato ricer into a bowl, add the sieved cocoa powder and the rum (if no children will be eating the Mont Blanc), combine well so you have a smooth mixture, which you will then leave to cool down. Whip the cream (it needs to be cold) and the icing sugar to stiff peaks. Take the chestnut mixture and put it through the potato ricer again. Heap it up in small bowls and, using a pastry bag, cover with whipped cream to create the effect of a snow-capped mountain and thus do justice to the name of the dessert!