Bring apple cider to a boil in saucepan over high heat. Reduce heat to medium and boil until it is concentrated and reduced to ¼ cup liquid; about 15 minutes. Set aside to cool.
In a large mixing bowl, whisk together flour, sugar, baking powder, baking soda, cinnamon, nutmeg, and salt.
In a separate bowl, whisk together buttermilk and eggs. Whisk in vanilla extract, and melted and cooled butter.
Pour apple cider reduction and wet ingredients into the dry flour mixture.
Mix ingredients together to form a soft round dough.
Line a baking sheet with parchment paper, Sprinkle with flour. Pat dough out to ⅜-inch to ½-inch thickness.
Freeze baking sheet with dough for 15 minutes or refrigerate for 1 hour.
In a large dutch oven or stockpot, pour in frying oil.. Heat oil to 350°F.
Cut donuts out with 3-inch donut cutter. Dip cutter into flour in between each cut. Pop out center donut rounds.
Reroll dough to produce about 18 donuts.
Fry 3 to 4 donuts at a time for about 1 minute on each side or until golden brown.
Place donuts on paper towel lined baking sheet.
Coat donuts in cinnamon and sugar mixture.