Preheat the oven to 350° F. Lightly grease a 10-inch tart pan with removeable bottom and set aside. In a mixing bowl combine the cookie crumbs, sugar, and melted butter. Stir the crumb mixture together until well combined.
Transfer the crumb mixture to the tart pan. Press the crumb mixture evenly on the bottom and sides of the tart pan. Bake for 5 minutes and then set aside to cool.
Chop the dark chocolate into small pieces and add to a mixing bowl. Heat 1 ½ cups of the heavy cream over medium heat until hot. When the cream is hot and beginning to bubble around the edges remove from the heat and pour over the chocolate. Let stand for a few minutes to allow the chocolate to melt.
Whisk together the chocolate and cream. When the chocolate mixture is completely smooth add ½ cup of the chestnut purée. Whisk until smooth.
Pour the chocolate chestnut filling into the cooled tart shell and shake gently to level the filling. Chill overnight or until firm.
To make the chestnut whipped cream topping, add the remaining 1 ¼ cups heavy cream to the bowl of a mixer fitted with a whip attachment. Begin beating the cream on high until soft peaks. Add the vanilla extract and the remaining ½ cup of chestnut purée. Continue beating until firm peaks.
Once the filling is firm, top with the chestnut whipped cream. If desired, use a piping bag to pipe the cream decoratively over the tart or simply pile the cream on top instead. Chill until serving and enjoy!