Boil the apple cider in a small saucepan until it is reduced to ⅓ cup. Set aside to cool down to 105F to 115F.
Add the 2 packets of yeast to the warm reduced apple cider. Mix and let rest for 5 minutes.
Warm the milk to about 100 degrees.
Put the milk, reduced cider-yeast mix, eggs, sugar, salt, cinnamon, nutmeg, butter and 2 cups of the flour in the bowl of your stand mixer.
Mix for 2 minutes at medium speed with the whisk.
Put the dough hook on and add 3 cups of flour and continue mixing dough for about 5 minutes.
Put the dough in a lightly oiled large bowl, cover with plastic wrap, and let it rise in a warm place until doubled in size, about 90 minutes.
Mix 1 cup of powdered sugar with about 2 tablespoons of apple cider to make the icing.
Heat the oil to 360 to 370F.
Roll out the dough until it is ⅓ to ½ inch thick.
Cut out the donuts using a donut cutter or a large jar and a small circular item.
Let the donuts rise until doubled in size, 20-30 minutes.
Fry several doughnuts at a time until golden brown, about 1 minute per side.
Remove the doughnuts and set on paper towels to drain.
While still warm, shake in a paper bag with cinnamon sugar or pour the glaze over them.