Apple Fritter Donuts

Ingredients:

For the Dough:
2¼ teaspoons (1 packet) active dry yeast
⅔ cup whole milk, warm to the touch
3¼ cups + 2 tablespoons all-purpose flour, divided
4 egg yolks
½ cup granulated sugar
⅓ cup apple cider
¼ cup unsalted butter, melted
1 tablespoon vanilla extract
1 teaspoon kosher salt
½ teaspoon ground cinnamon

For the Apples:
¼ cup unsalted butter
1 vanilla bean
7 Granny Smith apples, peeled, cored and chopped
¼ cup granulated sugar
½ teaspoon ground cinnamon
1 cup apple cider
¼ cup apple cider vinegar

For the Glaze:
½ cup + 2 tablespoons powdered sugar
¼ cup heavy cream
½ teaspoon vanilla extract
½ teaspoon kosher salt

2 quarts vegetable oil, for frying

Directions:
1. Make the Dough: Place the yeast in a mixing bowl. Pour the milk over the yeast a let sit for 5 minutes. Add 2 cups of the flour to the yeast and milk mixture, but do not stir. Cover the bowl with plastic wrap and set aside in a warm place until the surface of the flour cracks, about 30 to 40 minutes.

2. In a medium bowl, whisk together the egg yolks and sugar. Add the apple cider, melted butter, vanilla, salt, cinnamon, 1¼ cups of the flour and whisk until combined, then add to the yeast mixture. Using an electric mixer, beat the dough on low speed for 30 seconds, then increase the speed to medium and beat for 1 minute. Add the remaining 2 tablespoons of flour and mix on low speed for 30 seconds, then increase to medium for another 30 seconds. The dough will be VERY soft and sticky. Transfer the dough to an oiled bowl, cover the bowl with plastic wrap, and set in a warm place until the dough has doubled in size, about 1½ hours.

3. Make the Apples: Melt the butter in a 12-inch skillet over medium heat. Slice the vanilla bean in half lengthwise and scrape the seeds into the pan with the melted butter and drop the vanilla bean pod in as well. Heat the butter until it is bubbling, then add the chopped apples, tossing to coat them with butter. Add the sugar and cinnamon and cook for 5 minutes, stirring occasionally. Add the apple cider and vinegar, increase the heat to medium-high, and cook until all of the liquid has evaporated, stirring occasionally, about 10 to 15 minutes. Remove the vanilla bean and transfer the apples to a baking sheet to cool.

4. Assemble the Doughnuts: Scrape the dough out onto a well-floured surface and pat into a rectangle 2 inches thick, flouring the surface as necessary. Spread half of the apples over the dough, leaving space around the edges. Fold the dough into thirds (like a letter) by folding the bottom up and then the top down.