To begin, reduce the apple cider down to ½ cup. Do this by boiling over medium-high heat in a small saucepan for about 15-20 minutes.
To the reduced apple cider, add the butter and honey and stir until melted over low heat. Remove from the heat and pour into a large mixing bowl.
Add the applesauce, milk, and eggs to the bowl and stir to combine.
In a separate bowl, combine the flour, baking powder, baking soda, salt, cinnamon, and nutmeg and stir together. Add just enough flour to where the dough comes together. It will not be a typical bread dough and does not need to be kneaded. It should be wet and sticky, but still come together. If it is super wet, add some more flour. Keep in mind that it will harden somewhat in the fridge, making it easier to roll out.
Cover and place in the fridge for an hour.
In a deep pot, melt coconut oil or beef tallow. It should fill the pot about ⅓ of the way - enough so that the donuts don’t touch the bottom of the pot while frying.
Turn the dough out onto a floured surface and roll until it’s about ½ inch thick. Cut out the donuts using a 3-inch cookie or biscuit cutter. Then use something small to cut out the middles. Place on a baking sheet lined with parchment paper.
Combine the cinnamon and sugar in a bowl that is deep enough to dip the donuts in.
Make sure the oil has reached 350 degrees F. then place about 3 donuts in at a time. Fry for 30-60 seconds per side, until golden brown. Remove and place on a wire rack with a pan under it.
Pretty shortly after frying, dip the donuts into the cinnamon sugar mixture both sides. Make sure they are still a little moist so the coating sticks.