Preheat oven to 350 degrees.
Cut one of the tubes of cookie dough in half. Take one of the halves and scoop it into 6-8 mounds of dough and place them on a greased baking sheet. Bake cookies according to package directions. Set aside.
Let remaining cookie dough sit at room temperature for 10 minutes to soften.
Lightly grease a 13x9-inch baking pan. Press the remaining cookie dough into the bottom of the pan and bake at 350 degrees for 10-12 minutes. Dough will be soft and somewhat undercooked when you remove it from the oven, but if you cook it all the way, the cookie crust will get too hard when the dessert is refrigerated. Let cool.
Using an electric mixer beat cream cheese and sugar together until smooth. Fold in 2 cups of whipped topping. Spread on top of cookie layer.
Whisk together pudding mix and milk for 2 minutes. Pour evenly over cream cheese layer. Refrigerate for at least 2 hours. Top with remaining whipped topping. Crumble baked cookies and sprinkle on top.