For the ice cream cake: Bring the heavy cream to a simmer in a small pot. Pour the cream over the chocolate in a heatproof bowl and stir until smooth. Allow to cool 10 minutes before using.
Butter a 9-inch springform pan and line the bottom with a parchment paper circle.
Cover the bottom of the prepared pan with the brownies, using any extra pieces to line the sides of the pan if desired. Spread the chocolate ganache on top.
Scoop the ice cream onto the ganache layer, packing it in tightly. 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 of it, 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 chocolate whipped cream frosting: Add the heavy cream, chocolate syrup, confectioners' sugar and vanilla to a large bowl and whip with an electric mixer 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 chocolate whipped cream frosting, sprinkle with the cookies and drizzle with chocolate sauce. 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.