Pour the apple cider into a medium saucepan and heat over medium low until simmering. Allow the cider to simmer and reduce for ~40-45 minutes, until it's down to 1/2 cup. Remove from the heat and allow to cool for ~20 minutes.
While the cider is cooling, preheat the oven to 350°F and prep the dough.
Add the rice flour, baking powder, cinnamon, and nutmeg into a small bowl and whisk to combine.
In a large bowl, add the butter (make sure it's cooled a bit since melting) milk, both sugars, and vanilla. Whisk together until combined, and then whisk in the eggs. Once combined add the reduced apple cider.
Sift the dry ingredients into the large bowl of wet ingredients and fold together with a rubber spatula until fully combined. Rice flour can take a bit of time to accept moisture, so don't worry if this takes a bit of time to get the dough mixed smooth.
Spoon the dough into a Ziploc bag, or a piping bag if you have one. Generously grease a 4" doughnut pan, and pipe the dough into the pans, filling them until ~1/4" shy of the lip. Once all the doughnut wells have been filled, smack the pan down on the counter firmly a few times to help work out any air bubbles.
Bake for 10-13 minutes; a toothpick should come out clean.
While the doughnuts are baking, mix together the sugar and cinnamon for the coating in a medium sized bowl (make sure it's large enough to easily fit one of the doughnuts)
Once the doughnuts are done, remove from the oven and quickly and carefully release them from the pan onto a wire rack. Then, one at a time toss the doughnuts in the cinnamon sugar mix to coat. If the doughnuts are too hot to handle, use two forks to gently place it into the bowl and a spoon to scoop the sugar over top of the doughnuts. Repeat with the remaining doughnuts.
Allow the doughnuts to cool for ~10 minutes before serving.
Enjoy!
