In a skillet over medium to high heat, pour apple cider and applesauce. Bring to a simmer, stirring occasionally, and reduce to about 1/2 cup or 140g. This should take about 10 minutes. Set aside.
Pour oil into your pot, skillet, or deep fryer to heat up to 340 degrees F while you mix your donut batter.
In a medium bowl, whisk dry ingredients (mochiko, sugar, baking powder, salt, spices), then add wet ingredients (egg, reduced apple cider, melted butter) and mix well.
Use a two tablespoon cookie scoop to drop donut balls into hot oil (340 degrees F) and cook for 5 mins.
Remove donuts to a wire rack and when cool enough to touch, dunk in a bowl with extra cinnamon and sugar to coat.
Mochi donuts taste best the day they are made.