Cakey, dense baked donuts infused with concentrated apple cider and warm spices, then finished in melted butter and a cinnamon–apple pie spice sugar for an intensely autumnal bite.
Reduce the apple cider: In a small saucepan over low heat, simmer 1 1/2 cups apple cider, stirring occasionally, until reduced to about 1/2 cup, about 20 minutes. If there are spices/solids on top, leave them. Cool 10 minutes.
Preheat oven to 350°F (177°C). Lightly grease a donut pan.
Whisk dry ingredients: In a large bowl, whisk flour, baking soda, baking powder, cinnamon, apple pie spice, and salt.
Whisk wet ingredients: In a medium bowl, whisk melted butter, egg, brown sugar, granulated sugar, milk, and vanilla until combined.
Combine: Pour wet ingredients into dry, add the cooled reduced apple cider, and whisk until smooth; batter will be slightly thick.
Fill pan: Spoon or pipe batter into donut cavities, filling each about halfway.
Bake 10–11 minutes, until tops and edges are lightly browned and donuts spring back when lightly pressed.
Cool in pan 2 minutes, then transfer to a wire rack. Re-grease pan and bake remaining batter, if needed.
Make topping: In a medium bowl, combine granulated sugar, cinnamon, and apple pie spice.
Coat: When donuts are cool enough to handle, dunk both sides in melted butter, then coat generously in the spice sugar. Serve warm.
Storage: Donuts are best fresh. Store leftovers tightly covered at room temperature up to 2 days or refrigerate up to 5 days. Freeze up to 2 months.