Let the pie crust sit at room temperature for 15 to 20 minutes before starting. To blind bake the crust, transfer it to a 9-inch pie pan (save the parchment!) gently pressing it into the pan, into the corners and up the sides. Fold the edges underneath themselves to form a thick rim that hangs just over the edge of the pie pan. Place the crust into the freezer and chill for 30 minutes to one hour (you can also do this and leave it overnight, if you want to get this step done ahead of time).
Before you take the pie out, preheat the oven to 375°F. Prick the crust in several places with a fork. Line the inside of the crust with the parchment paper the dough was originally rolled with, then fill it with dry rice or dried beans. Bake the crust for 20 minutes, then carefully remove the parchment with the grains or beans inside. Return the crust to the oven and bake for another 18 to 20 minutes or so, until the crust is golden. Remove and let cool completely on a wire rack.
Take both ice creams out of the freezer and let soften slightly. In a medium sized bowl, combine the vanilla ice cream with 3/4 of the peanut butter cups, blending until they are well combined.
Scoop half of the chocolate ice cream into the cooled crust, spread it evenly, and smooth the top with an offset spatula or the back of a spoon. Turn the vanilla ice cream with the peanut butter cups on top of the chocolate ice cream (see Cooking Tip), and spread that out evenly, trying not to disrupt the bottom chocolate ice cream layer. Scoop the remaining chocolate ice cream on top, and smooth out that layer. Return the pie to the freezer to firm up completely, at least 3 hours, and up to 5 days. If you are storing the pie for more than a few hours cover the top tightly with plastic wrap.
Just before you are ready to serve the pie, place the cream, confectioners’ sugar, and vanilla in a mixing bowl. Use an electric mixer to blend the cream until firm peaks just form. Scoop the whipped cream attractively over the top of the pie. Let it sit for 10 minutes so soften just slightly before cutting. Use a sharp knife that has been dipped into a cup of very hot water, and then wiped dry to cut slices. Do this dip and wipe between each slice for the most attractive, clean slices.
If you want to make sure your layers are very even and unblended you can place the pie in the freezer for about 30 minutes between each ice cream layer addition, which will allow each layer to firm up before more ice cream is added. If you do this, keep the softened ice cream in the fridge while the pie is freezing between stages.