Preheat your oven to 350°F (175°C) and grease a donut pan.

In a medium bowl, combine the flour, baking powder, baking soda, cinnamon, nutmeg, and salt.

In another bowl, whisk together the apple cider, granulated sugar, brown sugar, applesauce, eggs, melted butter, and vanilla extract.

Gradually add the dry ingredients to the wet ingredients, mixing until just combined.

Pour the batter into a piping bag or a zip-top bag with the corner snipped.

Fill each donut cavity about 2/3 full with the batter.

Bake for 12-15 minutes, or until a toothpick comes out clean.

Allow the donuts to cool in the pan for 5 minutes before transferring them to a wire rack.

For icing, mix powdered sugar with a bit of apple cider until desired consistency is reached.

Drizzle the icing over the cooled donuts and enjoy!