Bring the apple cider to boil in a small saucepan over high heat. Boil for 1 minute and then reduce to medium heat. Stir the cider occasionally and allow it to gently boil until the liquid reduced by two-thirds, leaving one cup of liquid. This will take 15-20 minutes. Cool completely.
In a medium bowl, mix together the flour, baking soda, baking powder, salt, cinnamon, and nutmeg.
Using an electric mixer, cream butter and sugar on medium speed for 1 minute. Add eggs and beat an additional 1-2 minutes. Scrape the sides of the bowl and add in the vanilla extract, buttermilk, and the cooled cider. Mix on low speed until blended.
Pour the flour into the liquids and mix until flour is no longer visible. The dough should be thick and slightly sticky. Cover and refrigerate for 1 hour.
Turn dough onto a lightly floured surface and roll ½-inch thick.
Cut the dough using a donut cutter, or a 2 ½-inch biscuit cutter. If using a biscuit cutter, cut a 1-inch hole in the center using a small cutter or a knife. Reroll scraps to cut out additional donuts. Refrigerate dough in between rolling, if needed.
Heat oil in a large stock pan over medium-high heat until it reaches 360°F (182°C). Monitor the temperature using a frying thermometer to ensure the temperature is maintained between 360-375°F.
Working in batches, fry a few donuts at a time by placing the dough carefully into the oil. Cook for 1-2 minutes per side, until golden.
Transfer to a paper towel-lined plate and let cool for about a minute, then dip in the cinnamon-sugar bowl and sprinkle the donut to cover with cinnamon sugar.Serve while warm.
To make cinnamon sugar, simply mix 1 cup of granulated sugar with 1 tablespoon cinnamon.
Storage: Store donuts in an airtight container for 2-3 days. They can also be frozen for up to 3 months. Thaw frozen donuts at room temperature.Reheating: Leftover donuts can be warmed in the microwave for 30-60 seconds.Air Fryer: Make the donuts in the air fryer by cooking them at 330°F (166°C) for 8-10 minutes. Air fryer donuts will have more of a biscuit-like texture.The nutritional value of fried foods on the site is based on an estimation of 10% oil absorption. Actual oil absorption will vary depending on temperature, time, and oil type.