Line inside of a 9×5 inch loaf pan with plastic wrap. If using the ice cream between cake layers, line two round 8 or 9 inch cake pans with plastic wrap.
Pour condensed milk and flavorings (vanilla and peppermint) in a large mixing bowl.In a second bowl, whip the cream until thick. Fold the whipped cream into the condensed milk mixture, then pour into the loaf pan OR divide evenly between the cake pans. Cover with plastic wrap and chill for a few hours or until very firm.