Coat the interior of a 9-inch springform pan with butter. Place a circle of parchment in the bottom and butter it as well (I omitted this step and it didn’t stick).
Place the bowl of an electric mixer and wire whip attachment or the beaters in the freezer to chill.
To make the crust, place the broken cookies in the work bowl of a food processor fitted with the metal blade. Pulse until medium-size crumbs are formed. They won’t be uniform but don’t process long enough to make mush- just to grind the cookies into uneven crumbs. Leave the crumbs in the food processor.
Place the semisweet chocolate in a medium metal bowl. Pour the 1/2 cup heavy cream into a small saucepan; set over medium heat and bring the cream to a very gentle simmer. Pour it over the chocolate and stir until the mixture is smooth. Add two-thirds of the cookie crumbs; reserve the remaining crumbs. Stir the crumbs to coat them with the chocolate.
Spoon and scrape the mixture into the bottom of the prepared pan. Press the chocolate-coated crumbs evenly over the bottom all the way to the edge of the pan, but not up the sides. Set aside.
To prepare the filling, place the white chocolate and 2/3 cup of the heavy cream in a metal bowl placed over, but not touching, a pan of simmering water. Stir occasionally as the chocolate melts. When the mixture is smooth, remove it from over the water and set aside to cool.
In a chilled bowl using the chilled beaters, whip the remaining 1 1/3 cups of heavy cream and the vanilla until soft peaks form.
Pour 3 tablespoons of water into a small saucepan and sprinkle the gelatin over it. When the gelatin has softened, place the saucepan over very low heat and stir the mixture just until the gelatin has dissolved and liquefied. Immediately scrape the gelatin mixture into the white chocolate mixture, and fold gently until well combined. Fold the white chocolate-gelatin mixture into the whipped cream until the mixture is uniform. Scrape the filling into the prepared crust.
Refrigerate the torte until the gelatin has set, at least 4 hours or overnight (I refrigerated mine overnight).
To serve, loosen the edges of the torte from the sides of the pan with a small knife. Remove the sides of the pan and run a wide metal spatula between the bottom of the torte and the parchment liner, then lift the torte onto a flat serving plate. Just before serving, sprinkle the torte with the reserved cookie crumbs.
This torte can be refrigerated, covered, for up to 4 days.