Preheat oven to 350 degrees F. Line three 6-inch round cake pans with parchment paper. Grease lightly and set aside.
Whisk together flour, baking powder, and salt. Set aside. In the bowl of a stand mixer fitted with a paddle attachment, combined butter, coconut oil, and sugar. Add eggs and beat until mixture is pale in color. Scrape down bowl as needed to ensure thorough mixing.
Alternate adding flour mixture and milk, beginning and ending with the flour. Mix on low speed until combined. Fold in chopped cookie sandwiches.
Divide batter among the three prepared cake pans. Level batter and bake for 35-40 minutes until the cakes are golden brown and a toothpick inserted in center of cake comes out clean. Let cool in pan for 5 minutes before unmolding. Allow to cool to room temperature on wire rack.