Butter a 9-inch spring-form pan and line the bottom with parchment.
Cover the bottom of the pan with the chocolate chip cookies and then sprinkle with the crushed sandwich cookies. Scoop the cookies and cream and cookie dough ice creams onto the crushed cookie 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 spring-form pan and remove. Invert the cake onto a sheet of plastic wrap and remove the bottom of the pan and the parchment. Put a serving plate on the bottom and invert once more (so the chocolate chip cookie layer is on the bottom). Keep in the freezer until ready to frost.
For the chocolate ganache:
Put the chocolate in a medium heatproof bowl. Bring the heavy cream to a simmer in a small saucepan. Pour the cream over the chocolate and stir until smooth. Allow to cool 10 minutes before using.
Frost the top and sides of the cake with the ganache and top with the crushed 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 up to overnight. Let the cake sit at room temperature for about 20 minutes before slicing and serving.
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