- Position a rack in the center of the oven and preheat to 325 degrees. Use fingertips or a dry pastry brush to thoroughly grease the inside of a 10-inch light metal tube pan or 12-cup Bundt pan with the shortening. Dust with flour and tap out any excess. (Note: The Bundt pan makes a pretty fluted cake, but the pan’s heavy metal finish makes a thicker, chewier, and darker cake crust than will a light aluminum tube pan. Using a Bundt pan might also increase baking time by 5 to 8 minutes.)
- In small saucepan, simmer the cider until it reduces to 1 cup, about 30 minutes. Cool to room temperature.
- Sift together flour, salt, baking powder, cinnamon, mace, and cardamom into a medium bowl.
- Beat the butter until creamy in a large bowl with an electric mixer set to high speed. With the mixer running, gradually add the sugar and continue beating until the mixture is light and fluffy, about 5 minutes.
- Add the eggs one at a time, beating well after each addition. Quickly beat in the vanilla.
- Add the flour mixture in thirds, alternating with half the cider, beating after each addition only until the batter is smooth.
- Scrape the batter into the prepared pan. Gently tap the pan on the counter a few times to remove any trapped air bubbles. Bake in the center of the oven until a tester or wooden skewer inserted into the center of the cake comes out clean with a few moist, clinging crumbs, about 1 hour 10 minutes. Place the pan on a wire rack and let cool for 10 minutes. Turn out the cake and let cool to room temperature.
- Melt the butter in a medium saucepan over medium heat. Add the brown sugar and stir until smooth and bubbling. Add the cream in a slow, steady stream, stirring continuously. Cook, stirring occasionally, until the sauce thickens and comes just to a boil, about 5 minutes. Set aside to cool to room temperature. Stir in enough confectioners’ sugar to make a stiff glaze that resembles icing. Spoon the glaze over the cooled cake, letting it run down the sides. Sprinkle with pecans and let sit for a few minutes while the glaze sets.
- Bring the cider, Calvados, brown sugar, corn syrup, lemon juice, cinnamon, mace, and cardamom to a boil in a large saucepan over medium-high heat, stirring occasionally. (Don’t worry if lemon juice makes the mixture look curdled at first, just keep stirring.) Let cook at a low boil for 10 minutes.
- Stir in the cream and continue cooking until the mixture reduces to 1½ cups, about 1 hour, stirring occasionally. Remove pan from heat and stir in vanilla. Serve warm. (Make-ahead note: Cool, cover, and refrigerate sauce in a glass jar for up to two weeks. Reheat gently before serving.)
- Serve slices of cake with a little warm cider caramel sauce.