In a mixing bowl whisk together the dry ingredients: all purpose flour, baking powder, baking soda, cinnamon, ground nutmeg, and salt. Set aside.
Peel and core a sweet, medium to large sized apple. Shred using a cheese grater. Set aside.
In the bowl of a stand mixer with the paddle attachment or using a hand mixer add the melted butter, granulated sugar, egg, vanilla extract, sour cream, and 1/3 cup of the reduced apple cider you made earlier. Mix on medium speed for 30 seconds to a minute until combined. Add in the dry ingredients and the shredded apple. Mix on the lowest speed for about 30 seconds, until just combined.
Cover and place dough in the refrigerator for one and a half hours. Once your dough has chilled remove from bowl and place on a floured surface. The dough will be sticky so use plenty of flour on your hands and your working surface. Use a floured rolling pin to roll dough out to 1/2 inch thickness. Use a small cookie cutter or anything donut hole sized to cut donut holes out of the dough. Flour the cutting device in between each one to prevent from sticking. Place cut donut holes onto a parchment lined cookie sheet. When you run out of room to cut donut holes press dough back together and roll out again and continue repeating this until all or most of dough is cut into donut holes. Place cookie sheet containing donut holes into the refrigerator while you heat up your oil.
In a bowl mix together one cup cinnamon sugar and 1 tbsp cinnamon for coating donuts. Set aside.
In a large, deep pot or a dutch oven heat up a neutral oil such as vegetable or canola oil. Heat up enough to where the oil is three to four inches deep, in my dutch oven this was four cups of oil. Use a candy or deep fry thermometer to keep up with temperature of the oil. Heat oil to 365° to 375°. Once oil is preheated add donut holes four to six at a time. Fry for one minute and flip. Fry for another minute. Both sides should be golden brown and the donut holes should be floating. Remove with a slotted spoon and place on paper towels for about 30 seconds to a minute to cool down slightly. Roll in cinnamon sugar and place on wire rack while making the remaining donut holes.
After removing each set of donut holes check temperature of oil again and make sure to keep between 365° to 375° before adding next set of donut holes. Once all donut holes are fried and rolled in cinnamon sugar, make the glaze.