Bring apple cider to a boil in a saucepan over medium-high heat. Boil until reduced to about ⅓ cup. Transfer to a heat-proof bowl if desired. Stir in the apple butter. Set aside.
Whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, salt, and allspice. Set aside.
Whisk together the eggs, buttermilk, and the apple cider/apple butter mixture. Set aside.
Beat the butter, brown sugar, and granulated sugar with a stand mixer.
Stir in ½ of the flour mixture. Add ½ of the apple cider mixture and stir to combine. Repeat with the remaining dry and wet ingredients. (See notes for how to make baked donuts at this point.)
Turn onto a well-floured, parchment-covered baking sheet. Sprinkle additional flour on top of the dough. Flatten or roll out to about ¾ inch thickness. Cover and refrigerate for about 1 hour (or overnight).
Heat oil in a deep fryer (or use a large pot with a thermometer) to 360˚F.
Remove dough from the refrigerator. Use a 3 inch, floured doughnut cutter to cut out doughnuts. Save the donut holes and re-roll scraps. Return the cut donuts to the fridge until ready to fry.
Fry a couple of doughnuts at once for about 3 minutes, carefully turning halfway through cooking, until deep brown on both sides. Fry the holes for 2-3 minutes.
Drain on a paper towel lined plate. Coat with cinnamon sugar.
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Notes
One: Baked Donuts
Preheat the oven to 350˚F. After preparing the dough, transfer it to pastry bags (or gallon-sized ziptop bags) and cut off the tip. Pipe the dough into greased doughnut pans. Bake at 350˚F for 11-14 minutes. Transfer to a wire rack. Dip in melted butter and coat in cinnamon sugar.
Two: Mini Donuts
Use a mini donut butter and deep fry for 2-3 minutes. Or use a greased mini doughnut pan and bake for 8-10 minutes.
Three: Storage
Store in an airtight container at room temperature for 2-3 days or in the freezer for up to three months.Nutrition facts calculated with 1 cup of peanut oil. Your results may vary.