Glazed Apple Fritters

In the bowl of a stand mixer, whisk the yeast with the milk until dissolved. Let stand until foamy, about 5 minutes. Stir in 1 cup of the flour until a smooth paste forms. Cover the bowl with plastic wrap and let stand until doubled in bulk, about 1 hour.

In a small bowl, rub the vanilla seeds into the sugar. Attach the paddle to the stand mixer and beat the yeasted sponge at low speed until smooth. With the mixer on, gradually beat in the vanilla sugar. Beat in the egg yolks, salt and cinnamon, then beat in the apple cider and butter. Gradually beat in the remaining 2 cups of flour, beating until a sticky dough forms, 1 to 2 minutes. Scrape the dough into a greased large bowl. Cover with plastic wrap and let stand until doubled in bulk, about 2 hours. Refrigerate the dough until barely chilled, about 20 minutes.

In a very large skillet, melt the butter. Add the apples, apple cider, sugar, vinegar, lemon juice, cinnamon and vanilla bean and seeds. Cook over moderately high heat, stirring occasionally, until the apples are softened and most of the liquid has evaporated, about 8 minutes. Scrape the apples onto a large rimmed baking sheet to cool completely.

Scrape the dough onto a floured work surface and roll out to a 12-by-20-inch rectangle. With one long side facing you, spread half of the apple filling over two-thirds of the dough. Fold the remaining one-third of the dough over the filling, then fold it over again. Gently roll out the dough again to a 12-by-20-inch rectangle. Spread the remaining apples over two-thirds of the dough and fold as before. Cover the dough with plastic wrap and let stand until doubled in bulk, about 45 minutes.

In a medium bowl, whisk the confectioners’ sugar with the cream and cider until smooth.

Gently pat the dough into a 1/2-inch-thick rectangle, dusting with flour as needed. Cut the dough into 12 rectangles. Shape the rectangles into 4-inch ovals and transfer to a sheet of lightly floured parchment paper. Let stand for 10 minutes.

In a large saucepan, heat 2 inches of oil to 340°. Set a rack on a baking sheet. Carefully add 3 or 4 of the ovals to the hot oil and fry, turning occasionally, until puffed and deeply browned, about 8 minutes. Using tongs, transfer the fritters to the rack to drain. Repeat to fry the remaining fritters. Drizzle the glaze on top and sprinkle with salt. Let cool slightly before serving.