Place the Oreo cookies in a food processor and pulse until they become fine crumbs. Transfer the crumbs to a medium bowl and stir in the melted butter until well combined. Press the mixture firmly into the bottom of a 9×13-inch baking dish. Place the dish in the refrigerator to set while you prepare the next layer.
In a large mixing bowl, beat the softened cream cheese until smooth and creamy. Add the sugar and 2 tablespoons of milk, mixing until fully incorporated. Gently fold in 1 cup of the whipped topping. Spread this mixture evenly over the chilled cookie crust using a spatula.
In another large bowl, combine both packages of instant chocolate pudding mix with 3 1/4 cups of cold milk. Whisk vigorously for about 2 minutes until the pudding starts to thicken. Carefully spread the pudding over the cream cheese layer, smoothing the top as much as possible.
Let the pudding sit for 5 minutes to firm up slightly. Spread the remaining whipped topping over the pudding layer. Sprinkle the mini chocolate chips and holiday sprinkles evenly across the top to give it a festive look.
Cover the dish with plastic wrap or a lid. Place it in the refrigerator for at least 4 hours, or ideally overnight. This chilling time is crucial as it allows the layers to firm up enough to be sliced into clean squares.