Beat the cream cheese and sugar in a mixing bowl at medium speed until fluffy. Melt the heavy cream and the caramel together over a double boiler, stirring frequently. Set aside. Whisk the sour cream, eggs and vanilla together until completely combined. Slowly beat into the cheese until smooth. Mix in the melted caramel with a spoon then the apples, cinnamon and sugar.
Pour the apple filling into the prepared crust. Place on a sheet pan and put it in the oven. Pour some water on the sheet pan so it is ¼ of the way up the edge of the pan. Bake at 325°F for 1-½ hours, or until the toothpick comes out clean when inserted into the center. Serve well-chilled topped with a little of the reserved apple.