Cut a 5-by-24-inch rectangle out of parchment paper; set aside. Cut a 4-by-7 1/2-inch rectangle out of cardboard or Foamcore.
Using a spoon, spread 1 tablespoon chocolate ice cream across the cardboard. Arrange 16 sugar wafers over cardboard; we laid 10 wafers side by side over the lower half of the cardboard; then we made two rows of 3 wafers, laid end to end, over the top half of the cardboard. You should have a flat, single layer of wafers. This will become the bottom of the cake.
Microwave both chocolate and vanilla ice creams until softened, about 20 seconds. Transfer chocolate ice cream to a medium mixing bowl, and transfer vanilla ice cream to another one. Stir both ice creams with a rubber spatula; place the bowl of vanilla ice cream in the freezer.
Using a small offset spatula, spread 2 cups chocolate ice cream as evenly as possible over the wafer layer. Arrange 16 more sugar wafers, as described in step two, on top of the ice cream. Transfer the cake and the bowl of chocolate ice cream to the freezer for 15 minutes.
Remove the cake and the bowl of vanilla ice cream from the freezer. Stir ice cream with a rubber spatula to resoften it, and spread 2 cups vanilla ice cream as evenly as possible over wafers. Arrange 16 more sugar wafers, as described in step two, on top of ice cream. Transfer the cake and the bowl of vanilla ice cream to the freezer for 15 minutes more.
Repeat the layering process, making one more chocolate and one more vanilla layer, with only 1 wafer layer in between; chill the cake after making each new layer. End with the layer of vanilla ice cream on the top. Transfer cake to the freezer, and chill cake until completely hard, at least 1 hour.
Using a long serrated knife, trim 1/4 inch from all sides of the cake, making them even. Wrap the parchment around the sides of the cake, extending 1/2 inch above top layer; secure the seam with a small dollop of ice cream. Return cake to freezer.
Set a heat-proof bowl or the top of a double boiler over a pan of barely simmering water. Place the chocolate and the shortening in the bowl, and stir occasionally until melted, about 7 minutes. Remove the bowl from heat; let chocolate stand until cool but still liquid.
Remove cake from freezer, and pour melted chocolate over the top. Using a spatula, quickly spread chocolate so it meets all four edges of the paper collar. Sprinkle chopped peanuts over chocolate. Return cake to freezer, and chill cake until it has completely hardened.
When ready to serve, place cake on a serving plate, and remove the paper collar.