Heat apple cider over medium low heat. Simmer until the apple cider has reduced down to 1/2 cup (~40-45 minutes). Set aside to cool for 20 minutes.
Preheat oven to 350 degrees F.
Grease 2 donut pans and set aside.
Add sweet rice flour, baking powder, cinnamon, and nutmeg to a small bowl. Mix and set aside.
In a separate bowl, whisk together butter, vanilla extract, milk, light brown sugar, and granulated sugar. Add in the eggs and whisk until combined. Finally, add the apple cider concentrate from step 1 and mix.
Sift dry ingredients from step 4 into the bowl with the wet ingredients. Use a spatula to combine until you get a wet dough.
Spoon the dough into a pastry bag or Ziploc bag. Pipe the dough into the donut pans. I used a donut pan with donut molds that are 3 inches in diameter.
Smack the donut pan 1-2 times on a flat surface to get rid of some of the air bubbles.
Bake for 9-11 minutes until a toothpick comes out clean.
While the donuts are baking, make the cinnamon sugar topping. Combine sugar and cinnamon in a bowl. Mix and set aside.
Once out of the oven, cover the donuts in cinnamon sugar. Use 2 forks if the donuts are too hot to handle.
Cool on a cooling rack for 10 minutes before serving.