01 - Preheat oven to 350°F (175°C). Lightly grease two standard 6-cavity donut pans.
02 - Pour apple cider into a small saucepan. Bring to a boil over medium heat and simmer until reduced to 1/2 cup, approximately 10 to 12 minutes. Allow to cool before use.
03 - In a large mixing bowl, whisk together flour, baking powder, baking soda, ground cinnamon, nutmeg, allspice, and salt until evenly blended.
04 - In a separate bowl, blend reduced apple cider, granulated sugar, eggs, applesauce, melted butter, and vanilla extract until fully incorporated.
05 - Add wet ingredients to the dry mixture and stir gently until just combined. Avoid overmixing to maintain a tender crumb.
06 - Spoon or pipe batter evenly into prepared donut pans, filling each cavity approximately three-quarters full.
07 - Bake for 10 to 12 minutes, or until donuts spring back lightly when pressed.
08 - Allow donuts to cool in the pan for 5 minutes, then transfer to a wire rack to cool completely.
09 - Combine granulated sugar and ground cinnamon in a shallow bowl. Brush each warm donut evenly with melted butter, then coat thoroughly in cinnamon sugar.
10 - Serve donuts while fresh, or store in an airtight container at room temperature for up to two days.