Sift together the flour, baking powder, baking soda, salt, and spices into a medium bowl and set aside. In a mixing bowl cream together the butter granulated sugar, and brown sugar. Add the eggs one at a time and continue to mix until incorporated. Use a rubber spatula to occasionally scrape the sides and bottom of the bowl. Add the apple cider, buttermilk, and vanilla extract, mixing to combine. Add the flour mixture and combine.
Line a baking sheet with parchment paper and set aside.
Turn the dough out onto a lightly floured surface, and use a rolling pin to roll out the dough to 1/2 inch thickness. Lightly flour a doughnut cutter and use it to cut out the doughnuts, then place them onto the prepared baking sheet. Line a baking sheet with several layers of paper towels and set aside.
In a large heavy-duty pot, add enough shortening to equal 3 inches of oil. Heat to a temperature of 375 degrees F. Drop about 4 doughnuts into the oil, making sure not to overcrowd the pot. Cook for 1 to 2 minutes on each side, or until lightly golden brown. Remove the doughnuts from the oil and allow to drain on the paper towels.