Reduce the cider: Pour 1 1/2 cups of apple cider into a small saucepan and simmer over medium heat, stirring occasionally, until it reduces to 1/2 cup (about 15–20 minutes). It should be dark, syrupy, and smell intensely of apple. Let it cool to lukewarm.
Preheat the oven to 350°F (175°C). Generously grease a 12-cavity donut pan with butter or nonstick spray.
Whisk the dry ingredients: In a large bowl, whisk the flour, baking powder, baking soda, cinnamon, nutmeg, cloves, and salt.
Whisk the wet ingredients: In a separate bowl, whisk the granulated sugar, brown sugar, and eggs until pale and slightly thick. Whisk in the melted butter, buttermilk, vanilla, and the cooled reduced cider until smooth.
Combine: Pour the wet mixture into the dry and fold gently with a spatula just until no dry streaks remain — a few small lumps are fine. Overmixing makes tough donuts.
Pipe and fill: Transfer the batter to a piping bag or zip-top bag with a corner snipped off. Pipe into the donut pan cavities, filling each about two-thirds full.
Bake for 12–14 minutes, until the donuts spring back when lightly pressed and a toothpick comes out clean. The tops will look set and lightly golden.
Cool 5 minutes in the pan, then turn the donuts out onto a wire rack. While still warm, brush each donut lightly with melted butter, then toss in the cinnamon-sugar mixture until fully coated on all sides.
Serve warm for the best texture — the coating is at its crispest in the first couple of hours.