In a large saucepan, over medium-high heat, pour the apple cider and cook until the cider is reduced to 1 cup, about 20 minutes. Pour the cup of reduced apple cider in a small bowl and place into the refrigerator to cool.
Meanwhile, in a medium bowl, combine granulated sugar and 2 tablespoons of cinnamon. Set aside.
Next, in a large mixing bowl, add the flour, brown sugar, baking powder, salt, baking soda, nutmeg, and remaining cinnamon.
In a small bowl, lightly whisk the eggs. Add in the melted butter and cooled apple cider. Whisk until well blended. Pour over the flour mixture in the large mixing bowl.
Using a silicone spatula, stir to combine the wet and dry ingredients just until moist. Cover the bowl with a kitchen towel or plastic wrap and place in the refrigerator. Chill for 1 hour.
Flour a large work surface and place the donut dough in the center. With a lightly floured rolling pin, roll the dough into a large disc with a 1/2-inch thickness.
Use a traditional donut cutter or a 2 1/2 inch round biscuit cutter with a 1-inch biscuit cutter for the center hole to cut your donut rounds.
In a large pot, heat the oil over medium-high heat until it has reached a temperature of 375 degrees on a digital instant-read thermometer.
Working in batches of 4, carefully lower the donut rounds into the hot oil. Allow the donut to cook until golden and crispy, about 45 seconds to 1 minute per side.
Carefully remove the hot donuts with a slotted spoon to a paper-towel-lined plate, allowing excess oil to drain, for about 30 seconds. Next, quickly transfer the donuts to the bowl with the cinnamon-sugar mixture.
Using a spoon, coat the warm donuts in the cinnamon-sugar mixture. Place donuts on wire cooling rack to cool slightly. Serve immediately.