Cook apple in melted butter in large skillet over medium heat until tender, about 10 minutes, stirring occasionally. Stir in apple cider and apple pie spice; cover and simmer 5 minutes.

Whisk sweetened condensed milk and cream in medium bowl until well blended. Stir in apple mixture. Fill a large bowl about halfway with ice cubes and very cold water. Set the medium bowl containing the ice cream mixture inside the large bowl. Stir until very cold, about 5 to 10 minutes.

Freeze in ice cream maker according to manufacturer's instructions. Spread in 8- or 9-inch square pan. Cover and freeze until firm, about 3 hours. Scoop ice cream and mound in pan. Drizzle caramel topping over entire surface, allowing caramel to seep into ice cream. Pack ice cream back into pan. Cover and freeze until ready to serve.