Simmer the apple cider in a small saucepan over medium heat for 10 to 12 minutes, until reduced to about half a cup. Cool completely.
Preheat oven to 350 degrees F. Generously grease a Bundt pan, coating every groove.
Whisk the flour, baking powder, baking soda, cinnamon, nutmeg, cloves, and salt in a medium bowl.
In a large bowl, whisk the granulated sugar, brown sugar, and oil. Add eggs one at a time, then whisk in the applesauce, vanilla, and cooled reduced cider.
Fold the dry ingredients into the wet mixture just until no flour streaks remain.
Pour the batter into the prepared pan and bake for 50 to 55 minutes, until a toothpick comes out clean.
Cool in the pan for 15 minutes, then invert onto a wire rack to finish cooling.
While still slightly warm, brush the cake with melted butter, then roll or sprinkle it in the cinnamon sugar mixture until fully coated.