01 - Preheat the oven to 350°F. Lightly grease a donut pan.
02 - Simmer apple cider in a saucepan over medium heat until reduced to about 1/3 cup, approximately 10 to 12 minutes. Allow to cool.
03 - Whisk together flour, baking powder, baking soda, cinnamon, nutmeg, allspice, and salt in a large bowl.
04 - In a separate bowl, whisk the reduced apple cider, granulated sugar, brown sugar, eggs, melted butter, and vanilla extract until smooth.
05 - Pour the wet mixture into the dry ingredients and stir gently until just combined. Avoid overmixing.
06 - Spoon or pipe the batter into the prepared donut pan, filling each cavity approximately three-quarters full.
07 - Bake for 12 to 15 minutes until golden and a toothpick inserted comes out clean.
08 - Allow donuts to cool in the pan for 5 minutes, then transfer them to a wire rack.
09 - Combine sugar and cinnamon in a shallow bowl. Brush each warm donut with melted butter, then dip into the cinnamon-sugar mixture to coat evenly.