Special equipment: an 8 inch square baking pan
Put the chocolate in a small bowl and microwave in 20-second intervals, stirring after each interval, until melted, 1 to 2 minutes. Combine the mascarpone and the vanilla, 2 tablespoons of the heavy cream and 1/4 cup of the confectioners' sugar in a large bowl and stir to loosen the mascarpone slightly. Drizzle in the chocolate and stir until well mixed, with some flecks of chocolate (do not overmix or the mascarpone can get grainy).
Combine the granulated sugar and 2 tablespoons of the cocoa powder with 1 cup warm water in a medium bowl and whisk until the sugar is dissolved. Arrange half of the cookies in a layer in an 8-inch square baking pan, nestling the cookies on their sides and breaking cookies to fit as many as possible to cover the bottom of the pan. Spoon half of the cocoa water on top. Top with the mascarpone mixture and smooth evenly with an offset spatula. Top with the rest of the cookies and brush with the remaining cocoa water.
Combine the remaining 1 1 /4 cups heavy cream, 1/4 cup confectioners' sugar and 2 tablespoons cocoa powder in a large bowl and beat until the cream just holds stiff peaks. Spread the cream on top of the cookies. Cover with plastic wrap and refrigerate for at least 2 hours or up to overnight. Let stand at room temperature about 15 minutes before serving. Cut into squares and serve dusted with cocoa powder.