If using a stand mixer, fit with paddle attachment.
Warm the cider and milk. I do this in the microwave for about 20 seconds. It doesn't need to be hot (in fact, it should not be hot, we don't want to kill the yeast), just not cold from the fridge.*
Put the cider, yeast, shortening and milk in a large bowl (for stand mixer if you have one). Stir together or mix on low speed.
Add the eggs, sugar, salt, nutmeg, and half of the flour. Using the paddle attachment of your mixer (if you have one), combine the ingredients on low speed until flour is incorporated and then turn the speed up to medium and beat until well combined.
Add the remaining flour, combining on low speed at first, and then increase the speed to medium and beat well.
Change to the dough hook attachment of the mixer and beat on medium speed until the dough pulls away from the bowl and becomes smooth, approximately 3 to 4 minutes. If you do not have a dough hook/stand mixer – knead until the dough is smooth and tacky but not sticky.
Cover and let rise for 1 hour or until doubled in size.
On a well-floured surface, roll out dough to 3/8-inch thick.
Cut out dough using a 2 1/2-inch doughnut cutter or pastry ring or drinking glass and using a 7/8-inch ring for the center whole. Set on floured or parchment lined baking sheet. Cover (I do this with a floursack towel) and let rest for 30 minutes.
Pre-heat your air-fryer to 400 degrees Fahrenheit. My air fryer recommends pre-heating for 4 minutes.
While your air fryer is pre-heating, melt 8 tablespoons of butter in a small bowl. In a separate bowl, mix together 3/4 cup granulated sugar, 2 tablespoons cinnamon, and 1/2 teaspoon nutmeg.
When your air fryer is ready, lightly brush the top and bottom of the doughnuts with melted butter. Place the doughnuts in the preheated air fryer basket.
For doughnuts roughly 3 inches across, cook for 3 minutes, flip the doughnuts, and cook for 2 more minutes. (Smaller doughnuts need less time). For doughnut holes, cook for 2 minutes, shake, then cook for 1 more minute.**
When doughnuts come out of the air fryer, brush with more melted butter and dip into the cinnamon sugar mixture. Place on a parchment lined cookie sheet to cool.
To store place in a airtight container for 3-4 days.