In a small saucepan, simmer apple cider over medium heat until reduced to ¼ cup (15–20 minutes). Cool slightly.
In a bowl, whisk flour, baking powder, baking soda, cinnamon, nutmeg, allspice, and salt.
In another bowl, whisk melted butter, egg, sugars, buttermilk, vanilla, and reduced cider until smooth.
Fold dry ingredients into wet until just combined. Batter will be thick.
Preheat oven to 350°F (175°C). Grease donut pan. Fill wells about ⅔ full.
Bake 12–14 minutes, until tops spring back when touched.
Cool 5 minutes. Brush donuts with melted butter and roll in cinnamon sugar.
Enjoy warm with a cup of homemade apple cider!