In a food processor puree the chestnuts with enough confectioners' sugar to make it taste sweet. Add enough rum to make it the puree loose enough to fold into whipped cream; season with some instant espresso and vanilla. Chill until serving time.
Whip the cream and sweeten lightly with confectioner's sugar and chill until serving time.
Right before serving fold chestnut puree and cream together and transfer to serving glasses; garnish with shavings of bittersweet chocolate.