Apple Cider Doughnuts

2 red apples
2 1/2 cups apple cider
3 1/2 cup flour
4 tsp baking powder
1/4 tsp baking soda
3 1/2 tsp ground cinnamon
1 tsp salt
1/4 tsp ground nutmeg
1 2/3 cup sugar
3 tbsp shortening
1 egg
1 egg yolk
1/4 cup buttermilk
1 tsp vanilla
1/4 powder sugar
oil for frying

Core and chop the apples (leave the skins on). Combine with 1 1/2 cup cider in a medium sauce pan over medium heat; cover and cook until softened about 8 minutes. Uncover and cook until the apple are tender and the cider is reduced. Puree in a food processor until smooth.
Whisk the flour, baking powder, baking soda, 1 1/2 tsp cinnamon, salt, and nutmeg. Beat 2/3 cup sugar and the shortening. Beat in the egg and yolk, then gradually mix in the applesauce. Bean in half of the flour mixture, then the buttermilk and vanilla and then the rest of the flour. Refrigerate for at least 2 hours or overnight.
Heat 2 inches of oil to 350*. Cut the dough into circles and cut out the middle. Fry in oil for 1-2 minutes per side.

Glaze
Simmer 1 cup of cider in a pan over medium heat until reduced down to 1/4 cup. Whisk in powder sugar until smooth and glossy.