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1
Boil 1 cup apple cider in a small pot until reduced to 1/4 cup, about 10 minutes. Remove pot from heat and cool to room temperature.
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2
Beat white sugar and butter together with an electric mixer until creamy and smooth; add eggs, 1 at a time, beating well before each addition. Mix buttermilk and reduced apple cider into creamed butter mixture.
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3
Whisk flour, baking powder, baking soda, cinnamon, salt, and nutmeg together in a bowl. Slowly stir flour mixture into creamed butter mixture just until dough is combined.
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4
Turn dough onto a lightly floured piece of parchment paper. Sprinkle dough with flour and roll to 1/2-inch thickness, adding more flour if dough is sticky. Cut dough into doughnuts using a 3-inch-wide doughnut cutter and arrange on a baking sheet; refrigerate until chilled, 20 to 30 minutes.
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5
Heat at least 3 inches of oil in a deep-fryer or large saucepan to 350 degrees F (175 degrees C).
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6
Whisk confectioners' sugar and 2 tablespoons apple cider together in a bowl until glaze is smooth.
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7
Fry doughnuts in the hot oil, 2 to 3 at a time, until golden brown, 1 to 2 minutes per side; remove with a slotted spoon and drain on paper towels. Pour glaze over warm doughnuts.
