Bring chestnuts and 250 ml water to the boil in a saucepan. Cover and cook for 20 minutes, until almost all of the water has been absorbed. Stir occasionally. Add 200 ml of milk, sugar, 1 sachet of vanilla sugar, butter and salt. Simmer while stirring, about 40 minutes, until the chestnuts have crumbled. Pour in 6 tablespoons of milk.
Press the mass through a potato press. Cover and let cool down. Chop the couverture. Melt while stirring in a hot water bath. Let cool down. Whip the cream and 1 packet of vanilla sugar until stiff. Fill into a piping bag with a star nozzle.
Alternately distribute a little cream and chestnut mixture into glasses. Finish with cream tuffs. Drizzle the tuffs with liquid couverture. Let dry.