Cover 1 lb fresh chestnuts with water and set to boil. When the water boils, drain and peel the chestnuts, rub them through a colander, and mix with ½ glass fine sugar and 1 spoon cream. Rub through a coarse sieve to resemble fluffy kasha and pile around a small circular platter without pressing the purée. Fill the center with 1½ glasses thick whipped cream mixed with ½ glass fine sugar and vanilla.