For the crushed cookie crust: Preheat the oven to 350 degrees F. Butter a 9-inch springform pan and line the bottom with parchment.
Combine the melted butter with the wafer cookies in a medium bowl. Press the mixture into the bottom and up the sides of the prepared pan. Bake for 10 minutes, then let cool completely before using.
For the ice cream cake: Toss the strawberries with the sugar in a medium bowl and then layer them onto the cookie crust. Scoop the cookies and cream and strawberry ice creams onto the berry layer, packing it in tightly and alternating the scoops to create a marbled or checkerboard effect. Spread with an offset spatula to make a smooth top. Cover with plastic wrap and freeze until firm, 2 to 2 1/2 hours.
Unmold the cake by running a knife around the edge, then unhinge the springform and remove. Invert the cake onto a sheet of plastic wrap and remove the bottom of the pan and the parchment. Place a plate on the bottom and invert once more.
For the whipped cream frosting: Add the heavy cream, confectioners' sugar and vanilla to a large bowl and whip with an electric mixer on medium-high speed until soft peaks form. (This makes enough frosting to cover the top and sides of the cake with additional to pipe decorations if desired.)
Frost the top and sides of the cake with the whipped cream frosting, sprinkle with the wafer cookies. If the cake begins to get too soft, put it back into the freezer for a few minutes.
Freeze another 1 1/2 to 2 hours or overnight. Before serving, let the cake sit at room temperature for about 20 minutes.
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