Start by crushing 20 of the Oreo cookies into fine crumbs. Combine the crushed cookies with melted butter in a mixing bowl until well combined. Press the mixture firmly into the bottom of a 9x13 inch baking dish to form the crust.
In a separate bowl, whisk together the cold whole milk, chocolate pudding mix, and vanilla pudding mix until well combined. Let the mixture sit for about 5 minutes to thicken.
In another bowl, beat the cream cheese with an electric mixer until smooth. Add the granulated sugar and mix until fully incorporated. Gently fold in the pudding mixture until combined.
In a clean bowl, whip the heavy cream with the confectioner's sugar until stiff peaks form. Carefully fold the whipped cream into the cream cheese and pudding mixture until smooth and fluffy.
Spread half of the cream mixture over the prepared cookie crust in the baking dish. Crush the remaining Oreo cookies and sprinkle half of them over the cream layer. Add the rest of the cream mixture on top and smooth it out. Finish by sprinkling the remaining crushed Oreos on top.
Cover the dish with plastic wrap and refrigerate the Oreo Dirt Cake for at least 4 hours or overnight to allow the flavors to meld and the cake to set.
