Crumble prepared cake into a large bowl. Add vanilla icing and combine thoroughly.
Take 1 tablespoon of cake mixture and press it into the bottom of each divot in 2 ice cube trays. Spread 1 tablespoon vanilla ice cream over cake layer. Sprinkle about 1 teaspoon of crushed chocolate sandwich cookies on top of vanilla ice cream. Top with 1 tablespoon of chocolate ice cream.
Press the popsicle sticks into the centers of the ice cream cake pops. Freeze until hardened, at least 8 hours.
Using a butter knife, loosen the ice cream cake pops from the tray. Keep frozen until ready to serve. Enjoy!