Line the bottom of a 9-inch springform pan with parchment paper and lightly grease the sides, or add a parchment strip around the inside edge.

Unwrap the 12 Swiss rolls and cut each into slices about 1/2 inch thick. Pack the slices over the bottom of the pan and upright around the sides, keeping the chocolate coating facing outward; trim pieces as needed.

Crush 12–16 chocolate sandwich cookies into coarse crumbs and reserve the remaining cookies for garnish.

Spread about half of the slightly softened cookies-and-cream ice cream over the Swiss-roll base. Drizzle with about 1/3 cup hot-fudge sauce and sprinkle with half of the cookie crumbs.

Add the remaining ice cream and smooth the top. Cover and freeze for at least 4 hours, or overnight, until the cake is firm.

Let the frozen cake stand at room temperature for 5–10 minutes, then release the springform ring. Spread or pipe thawed whipped topping over the top and add cookie crumbs, chopped cookies, chocolate chips or shavings, and extra hot fudge.

Slice with a warm knife and serve immediately. If using homemade whipped cream, whip the cold heavy cream with powdered sugar until it holds firm peaks before decorating.