In a large saucepan, simmer the apple cider over moderate heat, stirring occasionally, until reduced to 1 cup, about 1 hour. Pour the reduced cider into a bowl.
Line a 9-by-13-inch rimmed pan with foil and coat the foil with nonstick cooking spray. In a medium saucepan, combine the heavy cream and condensed milk and bring to a simmer over moderate heat; keep the mixture warm over low heat.
In another large saucepan, combine the sugar with the reduced apple cider, corn syrup, water and salt and bring to a boil. Simmer over moderate heat until the sugar dissolves, about 5 minutes. Carefully whisk in the butter until melted. Gradually whisk in the warm cream mixture until incorporated. Cook over moderately low heat, stirring frequently, until a golden caramel forms and the temperature reaches 245° on a candy thermometer, about 45 minutes. Stir in the cinnamon, allspice and cloves and scrape the caramel into the prepared pan. Let cool completely, then refrigerate the caramel overnight.
Lightly brush a sheet of parchment paper with oil. Invert the caramel onto the parchment and peel off the foil. Using a sharp knife, cut the caramel into 1-inch-wide strips, then cut the block crosswise into 1/2-inch rectangles. Wrap each caramel in a square of parchment paper or a candy wrapper and twist the ends to seal. Serve or pack the caramels into boxes.