Bring cider to boil in 12-inch skillet over high heat; cook until reduced to 1 cup, 20 to 25 minutes. While cider is reducing, adjust oven rack to middle position and heat oven to 350 degrees. Grease and flour 12-cup nonstick Bundt pan. Whisk flour, salt, baking powder, baking soda, cinnamon, and allspice in large bowl until combined. Place confectioners’ sugar in small bowl.

Add 2 tablespoons cider reduction to confectioners’ sugar and whisk to form smooth icing. Cover with plastic wrap and set aside. Set aside 6 tablespoons cider reduction.

Pour remaining 1/2 cup cider reduction into large bowl; add melted butter, brown sugar, eggs, and vanilla and whisk until smooth. Pour cider mixture over flour mixture and stir with rubber spatula until almost fully combined (some streaks of flour will remain). Stir in apples and any accumulated juice until evenly distributed. Transfer mixture to prepared pan and smooth top. Bake until skewer inserted in center of cake comes out clean, 55 minutes to 1 hour 5 minutes.

Transfer pan to wire rack set in rimmed baking sheet. Brush exposed surface of cake lightly with 1 tablespoon reserved cider reduction. Let cake cool for 10 minutes. Invert cake onto wire rack and remove pan. Brush top and sides of cake with remaining 5 tablespoons reserved cider reduction. Let cake cool for 20 minutes. Then drizzle icing evenly over cake. Let cake cool completely, at least 2 hours, before serving. (Cooled cake can be wrapped loosely in plastic wrap. Store @ room temp.

NOTE: For the sake of efficiency, begin boiling the cider before assembling the rest of the ingredients. Reducing the cider to exactly 1 cup is important; if you accidentally overreduce it, make up the difference with water. To ensure that the icing has the proper consistency, we recommend weighing the confectioners’ sugar. We like the tartness of Granny Smith apples in this recipe, but any variety of apple will work. You can shred the apples with the shredding disk of a food processor or grater