Apple Cider Doughnuts

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This recipe is adapted from one I found on the food network.  Really, what 40+ week pregnant woman should be fussing with doughnuts, or the additional effort of rolling out dough and cutting the shapes out?  Insanity.  To cut down of effort, I knew that I would be making "doughnut holes," and I was actually hoping that I would be making this recipe after coming home from the hospital instead of before heading to.  So, I did the applesauce and glaze making in advance and froze them.  The recipe didn't specify whether to use spiced cider or not, so I opted for spiced. Finally, the original recipe calls for dipping the doughnuts in cinnamon sugar, which 1. was too sweet, and 2. I botched the recipe and added all the cinnamon to the dough, so I figured more cinnamon would be overkill.  It worked out in the recipe, however, so I've kept the extra cinnamon and I doubled the glaze because it wasn't quite enough for all the doughnuts.

2 Med. Apples (I used fuji)

3 1/2 C. Spiced Apple Cider, divided

3 1/2 cups all-purpose flour, plus more for dusting

4 teaspoons baking powder

1/4 teaspoon baking soda

3 1/2 teaspoons ground cinnamon

1 teaspoon salt

1/4 teaspoon freshly grated nutmeg

2/3 Sugar

3 Tbsp. Vegetable Shortening

1 large egg plus 1 egg yolk

1/4 C. Buttermilk

1 tsp. Vanilla

2 C. Powdered Sugar

Vegetable oil for frying

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Core and coarsely chop the apples (do not peel). Combine with 1 1/2 cups cider in a medium saucepan over medium heat; cover and cook until softened, about 8 minutes. Uncover and continue cooking until the apples are tender and the cider is almost completely reduced, about 5 minutes. Puree with an immersion blender or in a food processor until smooth. Measure the sauce; you should have 1 cup. (Boil to reduce further, if necessary.) Let cool slightly.

Whisk the flour, baking powder, baking soda, cinnamon, salt and nutmeg in a medium bowl.

Beat granulated sugar and the shortening in another bowl with a mixer on medium speed until sandy. Beat in the egg and yolk, then gradually mix in the applesauce, scraping the bowl. Beat in half of the flour mixture, then the buttermilk and vanilla, and then the remaining flour mixture. Mix to make a sticky dough; do not overmix.

Scrape the dough onto a lightly floured sheet of parchment paper and pat into a 7-by-11-inch rectangle, about 1/2 inch thick. Cover with plastic wrap and refrigerate for at least 2 hours or overnight.

Meanwhile, make the glaze: Simmer the remaining 2 cups cider in a small saucepan over medium heat until reduced to 1/2 cup. Whisk in the confectioners' sugar until smooth and glossy, then set aside.

Heat 2 inches of vegetable oil in a large heavy-bottomed pot over medium-high heat until a deep-fry thermometer registers 350 degrees. Line a baking sheet with paper towels. Cut the chilled dough into small (approx 1-inch) squares and shape into balls. Slip 4 or 5 doughnuts at a time into the hot oil and fry until golden brown, 1 to 2 minutes per side, adjusting the heat as needed. Transfer to the paper towels to drain.