Place the apple cider in a large saucepan over high heat and bring to a boil. Reduce to medium high heat and boil until reduced to 1-1/4 cup, about 20-25 minutes. For the cider into a glass jar and put it into the refrigerator until it is completely cooled.
In a small bowl, combine the white sugar and 1 tablespoon cinnamon and set aside.
In a large bowl, combine the flour, baking soda, baking powder, salt, nutmeg, cardamom and 1-1/2 teaspoons of cinnamon.
In a glass measuring cup or another bowl, whisk together 1/2 cup of the apple cider and the buttermilk.
In the bowl of a stand mixer with a paddle attachment, beat the dark brown sugar and the butter on medium speed until the mixture is pebbly. Add the eggs then beat the mixture on medium speed for about 1 minute until the mixture is lighter in color. Scrape down the sides and bottom of the bowl.
Add 1/3 of the dry ingredients and mix on low speed until combined. Add one-half of the cider-buttermilk mixture and mix on low speed until well combined. Add the remaining flour mixture in two additions alternating with the liquids and combine on low speed each time. Scrape the sides and bottom of the bowl and mix on low speed for another 10 seconds.
The dough will be very sticky, like cookie dough. Transfer the dough to another bowl, cover with plastic and place in the refrigerator at least 1 hour (or up to 24 hours).
Generously flour a cutting board (I use about 1/3 cup of flour) and place dough on cutting board. Sprinkle the top of the dough with flour and roll the dough to 1/2 inch.
Cut out 2-1/2-inch donuts. Fold the dough and re-roll it and out remaining donuts. I don't have a donut cutter so, I use a combination of a regular 2-1/2 inch cutter to cut out the donut and a 1/2-inch cutter to cut the donut hole.
Line a baking sheet with parchment paper and place the donuts on the parchment paper.
Heat vegetable oil in a large stockpot or Dutch oven over medium high heat until a deep-fry thermometer registers 360 degrees F. Line a baking tray with paper towels and place near the pot of oil. Place the bowl of cinnamon-sugar topping close to the baking tray.
Brush the excess flour from the donuts and carefully add them to the hot oil one at a time. Once the donut rises to the top of the oil, fry for about 60 seconds on each side or until deep brown on each side. Working in batches, add donuts to the pot and cook until evenly golden and crispy, Transfer to a paper towels and brush them with the remaining apple cider; then roll the warm donuts in cinnamon sugar mixture to coat.
Serve warm. If these are for the next day, allow the donuts to completely cool and place them in an air-tight container.