Reserve six cookies, process the others into fine crumbs, then measure 2 cups into a large bowl and mix with the crust confectioners’ sugar and melted butter before packing into a parchment-lined 13x9-inch pan. The moistened crumbs should hold together under pressure and form an even foundation.

Beat the softened cream cheese, filling confectioners’ sugar, and 1 cup cookie spread with a stand mixer fitted with a paddle attachment, then fold in 1-1/2 cups thawed whipped topping and spread over the crust. The filling should look uniformly pale caramel, without visible cream cheese lumps.

Combine the dry instant pudding mixes with the cold whole milk and heavy whipping cream in another bowl, whisk or beat with an electric hand mixer for 2 to 3 minutes, then distribute over the cheesecake filling. A smooth, thick mixture that leaves trails behind the whisk is ready to spread.

Cover the pudding with the remaining whipped topping, about 3 cups, then microwave the remaining 1/4 cup cookie spread in a small glass measuring cup for 30 seconds, cool slightly, drizzle over the surface, and draw a sharp knife tip through it. The spread should flow in thin ribbons without melting the topping beneath it.

Cover the assembled pan and refrigerate for at least 4 hours, or overnight for a firmer set. The fillings should hold their layers rather than flow when you begin cutting.

Finish with the extra cookie crumbs and, if desired, reserved whole cookies, then cut into squares. Each portion should show a compact crust beneath distinct creamy layers.