Prepare the GÄnoise a few hours ahead to let it cool off completely. Take the chestnuts and slice off a piece of skin (on the upper side). Boil the chestnuts in cold water. When cooked, skin them, put them through a food mill to make a paste. Stir the butter into the still warm paste. Make a syrup with the sugar and 1 cup of warm water. Add this syrup to the chestnut paste. Whisk in the rum and the vanilla sugar. Cut the GÄnoise into 3 slices horizontally. Make a syrup with 3 1/2 oz of slightly moist sugar cooked for 5 minutes and flavored, when cold, with the rum. Brush all 3 slices of the GÄnoise with this syrup. Spread the chesnut paste (1/3 inch thick) over each layer of cake. Assemble the layers, then cover the whole cake with the rest of the chestnut paste. Keep in the refrigerator for 30 minutes. Melt the white fondant icing, adding a tablespoon of water, over a very low heat. Place the cake on a rack and pour the white fondant icing starting with the center of the cake. Use a spatula to gather the excess icing, then pour a second layer of white fondant over the cake. Decorate with the glazed chestnuts. Keep refrigerated. This chestnut cake can be kept for a few days.
