Created by LindasBusyKitchen on March 6, 2015
Step 1: Place the yeast in a mixing bowl.
Step 2: Pour the milk over the yeast a let sit for 5 minutes.
Step 3: Add 2 cups of the flour to the yeast and milk mixture, but do not stir.
Step 4: Cover the bowl with plastic wrap and set aside in a warm place until the surface of the flour cracks, about 30-40 minutes.
Step 5: In a medium bowl, whisk together the egg yolks and sugar.
Step 6: Add the apple cider, melted butter, vanilla, salt, cinnamon, 1 1/4 cups of the flour and whisk until combined, then add to the yeast mixture.
Step 7: Using an electric mixer, beat the dough on low speed for 30 seconds, then increase the speed to medium and beat for 1 minute.
Step 8: 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.
Step 9: 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 1 1/2 hours.
Step 10: Melt the butter in a 12 inch skillet over medium heat.
Step 11: 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.
Step 12: Heat the butter until it is bubbling, then add the chopped apples, tossing to coat them with butter.
Step 13: Add the sugar and cinnamon, and cook for 5 minutes, stirring occasionally.
Step 14: Add the apple cider and vinegar, increase the heat to medium-high, and cook until all of the liquid has evaporated, stirring occasionally, about 10-15 minutes.
Step 15: Remove the vanilla bean and transfer the apples to a baking sheet to cool.
Step 16: 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.
Step 17: Fold the dough into thirds (like a letter) by folding the bottom up and then the top down.
Step 18: 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.
Step 19: 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.
Step 20: Meanwhile, in a large Dutch oven, heat the oil over medium heat to 375 degrees F.
Step 21: Scrape the dough out again onto a well-floured surface, and gently pat it out to 1/2 inch thickness, flouring the surface and the dough as necessary.
Step 22: Using a pizza cutter, bench scraper or sharp knife, slice the dough into 1 inch pieces in a checkerboard pattern.
Step 23: Shape 4 ounce portions of the dough into round mounds and allow to rest for 10 minutes.
Step 24: While the dough is resting, mix together the glaze.
Step 25: 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.
Step 26: Heat and whisk occasionally until the mixture is warm to the touch. Remove from the heat and keep warm.
Step 27: 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 4-5 at a time in my 7 1/4 quart Dutch oven).
Step 28: 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 4-5 minutes.
Step 29: Remove the doughnuts to a paper towel-lined pan or a cooling rack.
Step 30: Repeat with the remaining doughnuts, allowing the oil to come back up to temperature between batches.
Step 31: After removing each batch of doughnuts, allow them to sit for about 5 minutes, then brush with the glaze.
Step 32: Serve warm or at room temperature.