Pour the apple cider into a small saucepan and bring it to a boil over medium heat. Reduce the heat to low and let it simmer gently until it reduces to 1/2 cup, about 15 to 20 minutes. Remove from the heat and set aside to cool completely.

Preheat the oven to 350°F. Lightly grease two 6-well donut pans, with each well about 3 inches across, using nonstick baking spray or a little melted butter.

In a medium bowl, whisk together the flour, baking soda, baking powder, cinnamon, nutmeg, allspice, and salt until evenly combined. Set the dry mixture aside.

In a separate large bowl, whisk the avocado oil, egg, granulated sugar, and brown sugar until smooth. Add the applesauce, buttermilk, vanilla extract, and the cooled reduced apple cider, and whisk until the mixture is fully combined and glossy.

Add the dry ingredients to the wet mixture in two or three additions, folding gently with a spatula by hand until just combined and no dry streaks remain. Be careful not to overmix the batter.

Transfer the batter to a piping bag or a zip-top bag with one corner snipped off. Pipe the batter into the prepared donut pans, filling each mold about halfway full.

Bake for 10 to 12 minutes, until the donuts spring back when gently pressed and a toothpick inserted in the center comes out clean. Let the donuts cool in the pans for 3 to 5 minutes, then move them to a wire rack to cool until just warm.

For the coating, stir the granulated sugar and cinnamon together in a shallow bowl. While the donuts are still warm but comfortable to handle, brush each one lightly with melted butter, then roll it in the cinnamon-sugar mixture until completely coated on all sides.

Serve the donuts warm or at room temperature. They are best enjoyed the same day with a hot cup of coffee or a glass of apple cider.