Pulse the Oreos, including their filling, in a food processor or blender until they form coarse crumbs, leaving some larger bits if desired; stir in the melted butter. The mixture should look evenly moistened with visible cookie pieces rather than a fine, sandy powder.

Let the chocolate ice cream stand at room temperature for 10 minutes while lining a 9×3-inch or 10×3-inch springform pan with overlapping plastic wrap. Leave enough plastic wrap hanging over the rim to create handles for lifting the frozen cake later.

Spread the softened chocolate ice cream evenly across the lined pan with the back of a large spoon, then place the pan in the freezer for 30 minutes. The surface should feel firm when lightly touched through the plastic wrap, with no soft pool around the edges.

Bring the hot fudge to a room-temperature, spreadable consistency, then spread 1/2 cup over the firm chocolate layer and scatter the Oreo mixture evenly over it. The fudge should glide across the ice cream without steaming or turning the bottom layer soft.

Return the pan to the freezer for 30 minutes, and after 20 minutes set out the strawberry ice cream for 10 minutes. The cookie layer should become firm enough that crumbs stay in place when the next layer is added.

Drizzle the remaining 1/2 cup hot fudge over the cookie layer, then quickly spread the softened strawberry ice cream into an even top layer. Use gentle strokes so the strawberry ice cream stays distinct instead of pulling crumbs into the top layer.

Cover the pan with plastic wrap or aluminum foil and freeze for at least 12 hours and up to 2 days. The cake should be fully solid before removing the springform ring or applying frosting.

If transferring the cake from the springform base, place the serving plate, cake stand, or cutting board in the freezer for at least 30 minutes. A cold surface prevents the bottom ice cream layer from softening as soon as it touches the platter.

Beat the cold heavy cream, confectioners’ sugar, and vanilla with a handheld mixer or stand mixer on medium-high speed for about 4 minutes. Stop when the cream forms stiff peaks that stand upright without folding over.

Remove the pan rim, lift the cake with the plastic-wrap overhang, peel away the plastic, and set the cake on its springform base or chilled serving surface before frosting the top and sides. Keep the coating smooth or pipe a border, then add sprinkles if desired while the frosting is still soft.

Serve immediately, or freeze the frosted cake for up to 1 hour before serving, using a sharp knife warmed in hot water between cuts. Wipe the blade dry before each straight downward cut, then keep leftover cake covered in the freezer.