In a saucepan over medium or medium-low heat, gently reduce the apple cider to about 1/4 cup, 20 to 30 minutes. Set aside to cool.
Meanwhile, in a bowl, combine the flour, baking powder, baking soda, cinnamon, salt and nutmeg. Set aside.
Using an electric mixer on medium speed, beat the butter and granulated sugar until the mixture is smooth.
Add the eggs, one at a time, and continue to beat until the eggs are completely incorporated.
Use a spatula to scrape down the sides of the bowl occasionally.
Reduce the speed to low and gradually add the reduced apple cider and the buttermilk, mixing just until combined.
Add the flour mixture and continue to mix just until the dough comes together.
Line two baking sheets with parchment or wax paper and sprinkle them generously with flour.
Turn the dough onto one of the sheets and sprinkle the top with flour.
Flatten the dough with your hands until it is about 1/2 inch thick. Use more flour if the dough is still wet.
Transfer the dough to the freezer until it is slightly hardened, about 20 minutes.
Pull the dough out of the freezer.
Cut the doughnuts out using a doughnut cutter.
Place the cut doughnuts and doughnut holes onto the second sheet pan. Refrigerate the doughnuts for 20 to 30 minutes.
Add enough oil to a deep-sided pan and fry the doughnuts on medium heat till they turn golden brown (appx 30-60 seconds on each side) .
Drain onto an absorbant paper and leave it for a couple of minutes.
Sprinkle castor sugar over it and have it warm..