Cook apple in melted butter in a 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.

In a medium bowl, whisk sweetened condensed milk and cream until blended. Stir in the apple mixture. Fill a large bowl halfway with ice cubes and very cold water. Place the medium bowl containing the ice cream mixture inside the large bowl. Stir until very cold, about 5 to 10 minutes. (Alternatively, you can pour the mixture directly into an ice cream bowl and select the cooling mode only to chill the ingredients.)

Put the mixture in an ice cream bowl on ice cream mode. Spread it in an 8 - or 9 - inch square pan. Cover and freeze until firm, about 3 hours. Scoop the ice cream and mound it in the pan. Drizzle caramel over the whole surface, letting it seep into the ice cream. Put the ice cream back into the pan. Cover and freeze until ready to serve.