Pour the apple cider into a small saucepan over medium-high heat. Bring to a gentle boil and simmer for 10 to 12 minutes until reduced down to 1/2 cup of concentrated, dark amber cider. Remove from heat and allow to cool for 5 minutes.

Preheat your oven to 350°F (175°C). Generously grease two standard 6-cavity donut pans with nonstick baking spray. In a medium bowl, whisk together the flour, baking powder, baking soda, ground cinnamon, nutmeg, allspice, and salt until completely uniform.

In a separate large bowl, whisk together the melted butter, brown sugar, and granulated sugar until smooth. Whisk in the egg, buttermilk, vanilla extract, and cooled reduced apple cider until thoroughly combined. Pour dry ingredients into wet ingredients and fold gently with a spatula just until no dry flour pockets remain (do not overmix).

Transfer batter into a gallon ziplock bag and snip off the corner. Pipe the batter evenly into the prepared donut cavities, filling each about three-quarters full. Bake for 10 to 12 minutes at 350°F until the tops spring back lightly when pressed with a fingertip. Cool in the pan for 5 minutes, then transfer to a wire cooling rack.

Melt the remaining butter in a shallow bowl. In another wide shallow bowl, stir together granulated sugar and ground cinnamon. While the donuts are still pleasantly warm, generously brush each donut all over with melted butter, then dredge and roll thoroughly in the cinnamon sugar mixture until fully coated. Serve warm!