In a small saucepan, boil the apple cider over medium heat until it reduces to about 1 cup. This takes 35 - 45 minutes. Pour into a large heat proof mixing bowl and let cool to room temperature.
In a large mixing bowl, whisk the cooled cider with the brown sugar, white sugar, sourdough discard, eggs, and oil until smooth.
In a separate bowl, stir together the flour, baking powder, baking soda, salt, cinnamon, ginger, and nutmeg. Add the dry mixture to the wet and stir until a soft, sticky dough forms.
Cover and refrigerate for at least 2 hours or overnight, until firm and easy to handle.
Line a baking sheet with paper towels and place a wire rack on top. Mix the cinnamon sugar coating in a small bowl and set aside. Heat about 3 inches of oil in a Dutch oven or deep pot to 350°F (use a thermometer if you can).
On a well-floured surface, roll the dough to ½-inch thick. Cut out donuts using a donut cutter or round cookie cutters.
Fry a few donuts at a time, 1 - 2 minutes per side, until golden brown and puffed. Transfer to the rack to drain. Fry donuts holes for about 1 minute.
While warm, toss donuts in the cinnamon sugar mixture. Serve immediately, or see storage tips above. If using, top with vanilla glaze.