Preheat oven to 350 degrees Fahrenheit.
Grease the bottom of a 13x9 inch baking pan and fill with Oreo cookie halves - cream side up (set aside the other halves for later).
Prepare cake mix as directed and pour over Oreos in pan.
Bake cake according to instructions on box.
While the cake bakes, whisk together the Cookies & Cream pudding and 2 cups milk, taking care not to whisk it too long - it needs to be a pourable consistency.
While cake is still warm, poke holes in the cake with the end of a wooden spoon and pour the Cookies and Cream pudding over the top.
Allow the pudding to soak into the cake for about 2-4 minutes.
Place the cake in the fridge and allow to cool for about 30 minutes - 1 hour.
Whisk together the White Chocolate pudding and remaining 2 cups milk.
Add the Cool Whip.
Crush the remaining Oreo cookies (along with the halves from earlier in the recipe) and add half of the cookies to the Cool Whip/pudding mixture.
Spread the mixture on top of the cake and top with remaining crushed Oreos.
Chill for 1-2 hours before serving.