Crush 24 chocolate sandwich cookies into fine crumbs. Stir the crumbs with 6 tablespoons melted unsalted butter, then press the mixture firmly into the bottom of a 9-by-13-inch baking dish. Refrigerate the crust for 15 to 20 minutes.

Beat the softened cream cheese with 1/4 cup sugar, 2 tablespoons milk, and 1 teaspoon vanilla extract until smooth. Scrape the bowl as needed so the mixture is free of lumps.

Gently fold approximately 8 ounces of thawed whipped topping into the cream cheese mixture. Stir in several roughly chopped cookies from the remaining cookies.

Whisk one 3.9-ounce box of instant chocolate pudding mix with 3 1/4 cups cold milk for about 2 minutes, until the pudding thickens.

Spread the cream cheese mixture over the chilled cookie crust. Carefully spread the thickened chocolate pudding over the cream cheese layer.

Spread the remaining 8 ounces of whipped topping over the pudding layer. Smooth the surface gently so the layers remain distinct.

Crush or chop the reserved cookies and sprinkle them over the whipped topping. Cover the dish and refrigerate for at least 4 hours; overnight chilling is best for clean slices.