Pour the apple cider into a small saucepan and simmer over medium heat until it reduces from 1 1/2 cups to 3/4 cup, about 12 to 15 minutes. Pour into a measuring cup and let it cool slightly. Reserve 2 tablespoons of the reduction for the frosting.
Heat the oven to 350°F (175°C). Line a standard 12-cup muffin pan with paper cupcake liners.
Whisk the flour, baking powder, baking soda, salt, cinnamon, nutmeg, and cloves in a medium bowl.
In a large bowl, whisk the melted butter, granulated sugar, and brown sugar until smooth. Whisk in the eggs one at a time, then the applesauce, vanilla, and 1/2 cup of the cooled reduced cider.
Fold the dry ingredients into the wet ingredients in two additions, stirring just until no dry streaks remain. Do not overmix — a few small lumps are fine.
Divide the batter evenly among the 12 liners, filling each about two-thirds full.
Bake for 18 to 20 minutes, until the tops spring back when lightly touched and a toothpick inserted in the center comes out clean.
Let the cupcakes cool in the pan for 5 minutes, then transfer to a wire rack to cool completely, about 45 minutes. Frost only when fully cool.
To make the frosting, beat the cream cheese and butter in a large bowl until smooth and fluffy, about 2 minutes. Beat in the powdered sugar one cup at a time, then the reserved 2 tablespoons of cider reduction, cinnamon, vanilla, and salt until light and fluffy.
Pipe or spread the frosting onto the cooled cupcakes. Dust lightly with cinnamon sugar and top with a dried apple slice if you like. Serve at room temperature.