Preheat the oven to 350 °F and butter a 9x13 casserole pan. Set up three mixing bowls.
In a large bowl, sift together 1 cup flour, 1 1/2 tsp baking powder, and 1/4 salt. Separate egg whites and yolks into the other two bowls.
Beat egg yolks with 3/4 cup sugar with an electric mixer on high speed, until yolks are a pale yellow (2 minutes). Stir in 1/3 cup milk and 1 tsp vanilla.
Beat egg whites on high speed until soft peaks form (1 minute). With the mixer on, pour in remaining 1/4 cup sugar and beat on high speed until egg whites are stiff but not dry (1 minute)
Pour egg yolk mixture over the flour mixture and combine gently with a spatula. Add the Oreo crumbs and continue to delicately combine until incorporated.
Gently fold in egg white mixture with the spatula until just combined. Pour the batter into prepared pan, top with about ~24 oreos, spread evenly apart. Push them down into the batter a bit and use an offset spatula to smooth the risen batter over the top of the Oreos to cover them completely.
Add a second layer of cookies to top off the cake, this time using chocolate chip cookies. Set them atop the batter. Bake at 350˚F for 30-35 minutes or until a toothpick comes out clean.