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 tbsp vanilla extract
- 1 tsp 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 c 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 qt vegetable oil, for frying
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.
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.
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.
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.
Use your hands to again pat the dough into another rectangle about 2 inches thick. Spread the remaining apples on top and fold into thirds again.
Gather the dough together in a rough ball and return it to the oiled bowl. Cover and allow to rise until doubled in size, about 30 minutes.
Meanwhile, in a large Dutch oven, heat the oil over medium heat to 375 degrees F.
Scrape the dough out again onto a well-floured surface and gently pat it out to ½-inch thickness, flouring the surface and the dough as necessary. Using a pizza cutter, bench scraper or sharp knife, slice the dough into 1-inch pieces in a checkerboard pattern. Shape 4 ounce portions of the dough into round mounds and allow to rest for 10 minutes.
Make the Glaze:
While the dough is resting, mix together the glaze. Whisk together the powdered sugar, heavy cream, vanilla and salt in a medium bowl set over a small saucepan of simmering water over low heat. Heat and whisk occasionally until the mixture is warm to the touch. Remove from the heat and keep warm.
Fry the Doughnuts: Very carefully drop each mound of dough into the hot oil, only adding as many as will comfortably fit in the pot so they are not crowded (I found I could do 4 or 5 at a time in my 7¼-quart Dutch oven). Fry until the underside is golden brown, about 3 minutes, then using a spatula or spider skimmer, carefully turn them over and continue to cook until the other side is golden brown as well, another 4 to 5 minutes. Remove the doughnuts to a paper towel-lined pan or a cooling rack. Repeat with the remaining doughnuts, allowing the oil to come back up to temperature between batches.
After removing each batch of doughnuts, allow them to sit for about 5 minutes, then brush with the glaze. Serve warm or at room temperature.