Apple Cider Doughnuts

In a small saucepan, combine 1/4 cup plus 2 tablespoons of the fresh apple cider and the butter and bring to a boil over moderate heat. Stir in 1/4 cup plus 1 tablespoon of the flour and cook, stirring constantly, until a paste forms and pulls away from the pan, 1 to 2 minutes. Scrape the cider paste into a small bowl and let cool, then refrigerate until well chilled, about 2 hours.

In a blender, combine the cider paste with the cream, granulated sugar, eggs, vanilla bean paste and the remaining 1 cup of fresh apple cider and puree until smooth.

In a large bowl, whisk the remaining 4 1/4 cups of flour with the baking powder, salt and baking soda. Add the wet ingredients and, using a rubber spatula, stir until a sticky dough forms. Scrape the dough out onto a large baking sheet lined with plastic wrap. Cover with another sheet of plastic wrap and pat the dough 1 inch thick. Refrigerate until well chilled, at least 4 hours.

In a small saucepan, combine the granulated sugar with 1 tablespoon of water and cook over moderately high heat, swirling occasionally, until an amber caramel forms, 5 to 7 minutes. Remove from the heat and carefully add the cream and boiled apple cider syrup; the caramel will seize. Cook over moderate heat, stirring with a wooden spoon, until the caramel dissolves, about 2 minutes. Gradually add the butter and cook until thickened slightly, about 2 minutes. Stir in the salt. Scrape the mixture into a medium bowl and let cool completely. Whisk in the buttermilk and confectioners’ sugar until the glaze is smooth.

In a medium bowl, whisk the granulated sugar with the cinnamon and cardamom.

Remove the top sheet of plastic wrap and invert the dough onto a floured work surface. Peel off the plastic wrap and dust the dough with flour. Roll out the dough 1/2 inch thick. Using a 3-inch round biscuit cutter, stamp out 13 rounds. Using a 1-inch round cutter, stamp out the center from each round. Cut the scraps into 2-inch pieces. Transfer the doughnuts, holes and scraps to 2 baking sheets and refrigerate until chilled, about 30 minutes.

用一个大平底锅,热3英寸的菜籽油to 375° and top 2 baking sheets with racks. Keep the doughnuts chilled. Add one-third of the scraps at a time to the hot oil and fry, turning once, until browned, about 2 minutes per batch. Using a slotted spoon, transfer the scraps to a rack. Let the oil return to 375°. Add the doughnut holes and fry, turning occasionally, until browned all over, 1 to 2 minutes. Using a slotted spoon, transfer to a rack. Toss the doughnut scraps and holes in the cinnamon-cardamom sugar until coated and transfer to a platter.

Return the oil to 375°. In batches, fry the doughnuts, turning once, until browned, about 3 minutes per batch. Using a slotted spoon, transfer the doughnuts to a rack to cool for 10 minutes. Stir the glaze. Dip one side of each doughnut in the glaze and let stand until set before serving.