Take the ice cream out of the refrigerator and allow it to thaw on the counter while you prepare the crust.
In the bowl of a food processor, combine the whole package of cookies and the vegan butter. Process until thoroughly combined.
Line a springform pan (8 inches wide × 3½ inches deep) with parchment paper. To do so, cut one piece of parchment to the size of the bottom of the pan, and cut another strip to wrap around the sides.
Using your hands, evenly press the cookie mixture into a thin layer on the bottom of the pan. (This will leave the sides of the cake exposed so you can see the layers, but if you’re worried about the ice cream melting, you can press the cookie mixture up the sides of the pan, too, for a crust that will keep the ice cream well contained while serving.)
Scoop the vanilla ice cream out of the cartons and spread it into an even layer over the cookie mixture.
Evenly spread 2 cups of the chopped peanuts (or sandwich cookies laid flat) over the vanilla ice cream.
. Scoop the other-flavored ice cream over the peanuts and spread it into an even layer. (If you added cookie mixture to the sides of your pan and there is any excess reaching above the sides of the ice cream, cut the excess away so the cookie mixture is level with the ice cream cake.) Lay a piece of parchment paper over the open top of the springform pan, and press the parchment against the ice cream until it’s tightly packed.
Place the ice cream cake in the freezer and allow it to harden overnight or for at least 12 hours.
Remove the ice cream cake from the freezer, invert it onto a plate, and undo the springform pan. Flip the cake onto a serving plate or cake stand.
Top the cake with any of the optional decorations. Serve the cake immediately or return it to the freezer until you are ready to serve.