Chocolate Chip Cookie Delight

tube (16-1/2 ounces) refrigerated chocolate chip cookie dough

package (8 ounces) cream cheese, softened

confectioners' sugar

carton (12 ounces) frozen whipped topping, thawed, divided

cold 2% milk

package (3.9 ounces) instant chocolate pudding mix

package (3.4 ounces) instant vanilla pudding mix

Chopped nuts and chocolate curls, optional