Place two medium to large bowls in the freezer to chill for 20 minutes. Line a 9” square pan with plastic wrap or parchment paper, and set in the freezer as well.
In a chilled bowl, use a hand mixer to beat the vegan heavy cream from the peanut butter filling section into stiff peaks. Add in the powdered sugar and vanilla extract, and mix until incorporated. Then add in the peanut butter and vegan cream cheese, and mix again until creamy. Set aside.
In the remaining chilled bowl, use a hand mixer to beat the vegan heavy cream from the chocolate filling section into stiff peaks. Add in the cocoa powder and powdered sugar, and mix until incorporated. Be careful, as cocoa powder can spray up before fully incorporated, so start slow then increase speed.
Remove the pan from the freezer. Spoon half of the peanut butter batter into the loaf pan, and spread to be smooth. Dip an Oreo into the dairy free milk, and place on top of the peanut butter layer. Repeat until the peanut butter layer is fully covered (about 12 Oreos- you may need to slice them in half to fit, like I did. See post photos). Then spoon all of the chocolate batter on top, and spread smooth. Place another layer of dairy free milk soaked Oreos on top. Finally, spoon the remaining peanut butter ice cream layer on top, and smooth to finish. You can add an extra layer of Oreos here if desired.
Freeze: Place the peanut butter Oreo icebox cake into the freezer to chill for 3+ hours, or overnight.
Make a batch of vegan chocolate ganache. Wait for the ganache to cool 20 minutes so it doesn’t melt the icebox cake, and rather sets perfectly on the chilled cake top.
Remove the icebox cake from the freezer. Place a piece of parchment paper down on top of the cake, along with your serving plate. Carefully flip the cake over so that the plate is now on the bottom and the cake is flipped upside down, with the pan on top. Carefully remove the pan, and peal away the parchment paper. Pour the chocolate ganache on top, and decorate with chopped vegan peanut butter cups, crushed Oreos, and a drizzle of peanut butter.
Slice immediately and enjoy. Store the cake in the freezer after about 20-30 minutes. Enjoy!