Pour apple cider into a medium-sized saucepan and cook over medium heat until the liquid has been reduced to just ¾ cup (175ml). You will need to keep a liquid measuring cup handy and pour the cider back into the measuring cup to be sure it has reduced enough. How long this takes will vary depending on your particular stovetop, for me it usually takes about 10 minutes.
Allow apple cider to cool completely before proceeding. You can speed this up by placing it in the refrigerator. If you prepared the apple cider in advance, simply store covered in the refrigerator.
Preheat oven to 350F (175C) and lightly grease a 12-count donut pan with baking spray. Set aside.
In a large bowl, whisk together flour, sugars, cornstarch, baking powder, baking soda, salt, cinnamon, nutmeg, and allspice until well-combined.
In a separate bowl (I like to use a large measuring cup), whisk together reduced apple cider, egg, and vanilla extract. Stir in melted butter (this will separate from the cider, that’s fine).
Pour liquid ingredients into dry ingredients and use a spatula to gently stir everything together until just combined (don’t over-mix or your donuts will be dense and dry).
Spoon or pipe batter evenly into prepared donut pan (I like to pour the batter into a large piping bag or large Ziploc bag and then just snip off one corner for easy piping).
Transfer to 350F (175C) oven and bake for 9-10 minutes or until a toothpick inserted in the thickest part of the donut comes out clean or with a few moist crumbs.
Allow donuts to cool in the pan for 5 minutes then carefully remove to a cooling rack.
Whisk together granulated sugar and cinnamon in a shallow dish and set aside.
Use a pastry brush to lightly brush donuts on both sides with melted butter and then immediately dip on both sides in cinnamon/sugar mixture.
Serve warm! Donuts will keep in an airtight container for up to two days but are hands-down best served warm.