Crush chocolate cookies into fine crumbs using a food processor or place in a zip-top bag and crush with a rolling pin.
Mix cookie crumbs with melted butter until the mixture resembles wet sand. Press firmly into the bottom of a 9x13 inch dish to create an even layer.
Place the crust in the refrigerator while preparing the next layer.
For the cream cheese layer, beat the softened cream cheese until smooth and fluffy. Add sugar, milk, and vanilla, continuing to beat until well combined.
Fold in half of the whipped topping (about 4 ounces) with a gentle hand.
Spread this mixture evenly over the chilled crust.
For the chocolate pudding layer, whisk together the pudding mixes and cold milk until it begins to thicken, about 2 minutes.
Pour the pudding over the cream cheese layer and spread gently to create an even layer.
Return the dish to the refrigerator for about 5-10 minutes to allow the pudding to set slightly before adding the final layer.
Spread the remaining whipped topping over the pudding layer, creating decorative swirls if desired.
Garnish with chocolate curls, mini chips, or additional cookie crumbs.
Refrigerate for at least 4 hours or overnight before serving.