Preheat oven to 325 degrees F (165 degrees C). Grease a 9x13-inch cake pan or baking dish.
Process chocolate chip cookies in a food processor until completely crumbled. Add sugar, flour, baking powder, and cinnamon to cookie crumbs; pulse to combine. Add butter, eggs, and vanilla to cookie mixture; process until blended.
Pour milk into cookie mixture while food processor is running; blend until batter is evenly mixed. Pour batter into prepared pan.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 40 minutes. Cool in the pans for 10 to 15 minutes.
