Preheat the oven to 350 degrees F.
Spray 2 (9-inch) cake pans with cooking spray and dust with flour.
In a large bowl, using a hand-held mixer, combine the flour, cocoa, sugar, baking powder, baking soda, and salt. Add the eggs and egg yolk, 1 at a time, and beat until well mixed, then add in the melted butter and combine. Next, add the buttermilk and beat until smooth, about 2 to 3 minutes. Add in the crumbled cookies and beat until incorporated.
Pour the batter evenly into the cake pans and bake until a toothpick inserted in the center of the cake comes out clean, about 30 to 35 minutes. Remove from the oven and cool, on a rack, in the pans for 5 minutes. Turn the cakes out onto a rack and let cool completely. Frost with Cookies and Cream Cheese Icing and serve.
In a large bowl with an electric mixer, blend the butter and cream cheese until smooth, about 3 minutes. Add the salt and vanilla. Add in the confectioners' sugar, 1/2 cup at a time, until smooth. Beat in the crumbled cookies. Frost the chocolate cookie cake when the cake has cooled.