- Pour cider into a small pan over medium heat. Reduce by half, then set aside to cool.
- In the bowl of a mixer fitted with paddle attachment, beat butter and ¾ cup sugar on medium speed until light in color. Scrape sides of bowl with a rubber spatula. Add eggs and turn on mixer, beating until incorporated. Scrape sides again with rubber spatula.
- In a small bowl, stir to combine cider, buttermilk, and maple syrup. In a medium bowl, whisk to combine flour, salt, baking powder, baking soda, and spices. Scoop ⅓ of dry ingredients into mixer. Mix on low speed until incorporated, then add ½ of cider mixture and mix on low until incorporated. Scrape sides of bowl with rubber spatula and repeat, ending with dry ingredients. Mix on low until dough forms.
- Transfer dough to a sheet pan and chill in freezer 5 to 10 minutes. Meanwhile, pour oil into a medium pot over low heat.
- In a medium bowl, stir to combine 1 cup sugar and 2 tablespoons cinnamon. Reserve.
- Remove dough from freezer and place on a floured work surface. Roll to ½-inch thickness and cut using a 3-inch round cutter. Use a smaller cutter to remove center of round. Transfer cut dough to a clean sheet pan and reserve in refrigerator until ready to fry.
- Increase heat on stove to medium and heat oil to 360 degrees. Gently place doughnuts in oil, being careful not to overcrowd pot. Fry until golden, approximately 4 minutes, then transfer to paper towels to drain. Toss in bowl of cinnamon-sugar to coat. Serve warm.