Pulse the Oreos in a food processor until they form fine crumbs; alternatively place cookies in a resealable bag and crush with a rolling pin.
Mix the Oreo crumbs with the melted butter until evenly moistened, then press the mixture firmly into the bottom of a 9 x 13-inch baking dish to form the crust.
Chill the crust in the refrigerator for a few minutes while you prepare the filling.
In a mixing bowl, beat the room-temperature cream cheese until fluffy. Add the 2 tablespoons milk and the powdered sugar, then beat until smooth and combined.
In a separate bowl, whip the heavy cream with an electric mixer until soft peaks form, then fold the whipped cream gently into the cream cheese mixture until uniform.
Spread slightly less than half of the cream cheese mixture over the chilled Oreo crust in an even layer.
Whisk the two chocolate pudding mixes with 3 1/4 cups cold milk until thickened, then spread the pudding evenly over the cream cheese layer and chill for 5–10 minutes to set slightly.
Carefully dollop the remaining cream cheese mixture over the set pudding layer and use an offset spatula or rubber spatula to smooth it into an even top layer.
Sprinkle the mini chocolate chips evenly over the top of the dessert.
Chill the assembled dessert for several hours or overnight until fully set before slicing and serving.