Coat 8 x 4-inch soufflé dish (2-1/2 quarts) with nonstick vegetable-oil cooking spray. Line inside of dish with plastic wrap, using 4 pieces of wrap, overlapping if necessary, and leaving at least 3 inches of overhang all around the edge of the soufflé dish.
Let the strawberry ice cream and vanilla ice cream soften at room temperature for 15 minutes or until consistency of cream cheese.
Slice the cake in half horizontally. Press the top half of the cake with crumbs, cut side down, into the bottom of the prepared soufflé dish (it will fit snugly).
Spread 1/2 cup of the fudge sauce evenly over the crumb layer. Top with the strawberry ice cream, gently spreading to the edge of the dish. Spread the chopped cookies over the top of the ice cream; press the cookie pieces gently into the ice cream. Carefully spread 1/2 cup fudge sauce over cookies, being careful not to move the cookie pieces. Spread the vanilla ice cream over the fudge sauce. Press second cake layer, cut side up, into soufflé dish onto vanilla ice cream. Cover cake with plastic wrap overhang. Transfer soufflé dish to freezer. Freeze overnight.
Use plastic wrap to lift cake out of dish; if necessary, loosen edge of cake with spatula. Unwrap plastic and discard; place cake on platter. Spread top with remaining 1/2 cup fudge sauce; sprinkle with reserved chopped cookies. Cut into 12 slices. Serve immediately. To save any remaining slices, tightly wrap with clean plastic wrap and freeze -- no need to return them to soufflé dish.