Line a 9-inch (23 cm) springform pan with parchment paper, covering the bottom completely to make removal easier after freezing.
Add the chocolate sandwich cookies to a food processor and pulse into fine crumbs. Pour in the melted butter and pulse again until the mixture is evenly moistened and holds together when pressed.
Transfer the crumb mixture to the prepared pan and press it firmly into an even layer across the bottom. Use the bottom of a glass or measuring cup to compact it well so the crust sets up solid and doesn’t crumble when sliced. Freeze for 10 to 15 minutes.
Let the ice cream sit at room temperature just until it softens enough to spread. It should be spreadable but not melted, which helps it refreeze smoothly without forming icy patches.
Spoon the softened ice cream over the chilled crust and spread it into an even layer, keeping it level from edge to center. Aim for about ¾ to 1 inch (2 to 2.5 cm) thick to keep a pizza-like look.
Cover and freeze for at least 2 to 3 hours, or until fully firm.
Once frozen solid, keep the ice cream in the pan and use a knife or offset spatula to lightly mark/draw a circle about ½ inch (1.25 cm) inside the edge. Carefully trim away/pick out that outer ring of ice cream while it is still in the pan to expose a clean border of cookie crust.
Release and remove the outer ring of the springform pan, then transfer the base to a serving surface.
Add toppings evenly over the surface, pressing lightly so they adhere to the frozen layer. Add a dollop of whipped topping and a marashchino cherry if you like. Drizzle with chocolate or caramel sauce if using.
Run a sharp knife under warm water, wipe it dry, and cut into wedges. Clean and warm the blade between cuts for smoother slices. Serve immediately while firm.