Leave the ice cream pints at room temperature for 15 minutes to soften, making them easier to spread.
Remove the cake from its pan and place it on a cutting board. Using a sharp or serrated knife, carefully slice the cake horizontally into three even layers. You can use a ruler to ensure uniform layers.
Line the empty cake tin with a large sheet of saran wrap making sure there is enough overhang to wrap the cake before freezing.
Place the bottom cake layer in the cake tin. Scoop out the pistachio ice cream from the first pint and spread it evenly over the cake layer. Sprinkle one-third of the pistachios over the ice cream layer.
Repeat the above process with the second cake layer, adding ice cream and pistachios. Add the top cake layer and gently press it down.
Wrap the cake tin tightly with plastic wrap and freeze for at least 8 hours or up to a few days.
When ready to serve, remove the cake from the freezer and unwrap it. Stretch the aluminum pan to release the cake, or run a knife around the edge to free it onto a serving dish or cutting board.
Spread an even layer of Cool Whip over the top and sprinkle with the remaining pistachios. Using a sharp bread knife, cut the ice cream cake into 1-inch slices and serve.