Reduce the apple cider by pouring 2 cups into a small saucepan and simmering over medium heat until it reduces to about ½ cup, approximately 20-30 minutes. Set aside to cool completely.
Preheat your oven to 350°F (175°C) and generously grease your donut pan with non-stick spray or butter.
Whisk together the dry ingredients in a medium bowl: flour, baking soda, baking powder, cinnamon, nutmeg, allspice, and salt. Set aside.
In a large bowl, combine the wet ingredients by whisking together the melted butter, oil, brown sugar, and granulated sugar until smooth. Add the eggs one at a time, mixing well after each addition, then stir in the vanilla extract and cooled cider reduction.
Gradually fold the dry ingredients into the wet mixture until just combined. Be careful not to overmix – a few small lumps are fine.
Transfer the batter to a piping bag or ziplock bag with a corner snipped off, and pipe into the donut cavities, filling each about ⅔ full.
Bake for 10-12 minutes until the donuts spring back when lightly touched and a toothpick inserted comes out clean.
Allow the donuts to cool in the pan for 5 minutes, then transfer them to a wire rack.
While still warm, brush each donut lightly with melted butter and immediately roll in the cinnamon-sugar mixture to coat all sides.
Serve while still slightly warm for the most authentic cider donut experience.