Double line a 9-inch square baking pan with foil, leaving 2 handles extended over the sides.
Pulse the cookies in a food processor until fine. Toss the cookies and butter in a medium bowl. Firmly press the cookie crumbs into the bottom of the prepared pan.
Carefully spread the softened ice cream across the crust. Drizzle with the caramel and top with the whipped topping. Sprinkle with a dusting of shaved chocolate. Place in the freezer for 3 hours to firm up.