Preheat the oven to 325 degrees F. Add butter, shortening, and granulated sugar and mix for 2 minutes. Add eggs and vanilla and mix.
Add flour, cornstarch, salt, baking powder, and mix until just combined. Add crushed Oreos and mix (the dough should be very soft).
Using a large cookie scoop, scoop out about 1/2 cup of dough per cookie, with 6 total on a lined baking sheet. Before putting in the oven, flatten each dough ball slightly.
Bake at 325 degrees F for 12-15 minutes. Cookies should look barely set. Transfer the cookies automatically to the fridge and let them cool completely.
Cookies n' Cream Frosting
Mix the butter for 2 minutes, then add the confectioner's sugar and vanilla and mix again. While it is mixing, slowly add the milk until it's smooth.
When the cookies are completely cooled, frost each cookie and put them back in the fridge. Keep the cookies in the fridge until right before serving so they're nice and cool!! Enjoy!