Preheat the oven to 350 degrees F. Butter and flour 5 (9-inch) cake pans. Set aside.
In a medium bowl, stir together flour, baking soda, 1 teaspoon cinnamon, ginger, 1/2 teaspoon nutmeg, and salt. In a large bowl, using a wooden spoon, mix together 1/2 cup butter and the brown sugar until creamy. Add sorghum and eggs, and beat until well combined.
Add dry ingredients in 3 batches to butter mixture, alternating with buttermilk, beginning and ending with the dry ingredients. The batter will be very stiff. Divide it equally among prepared pans, spreading it out evenly with an offset spatula.
Bake until a wooden skewer inserted in the center comes out clean, 15 to 20 minutes. Transfer pans to a wire rack to cool for 10 minutes, then invert cakes onto racks and let cool completely. (The cake layers will be thin, only about 1/2-inch high.)
While cake is baking, make the filling; combine dried apples with cider or water in a heavy saucepan over low heat. Bring to a gentle simmer, cover, and cook until apples are the consistency of relatively thick preserves. This will take anywhere from 20 minutes to 1 hour, depending on how dry the apples are. Add more liquid as necessary to achieve correct consistency. Flavor with cinnamon or nutmeg, if desired. Remove from heat, and let cool.
To assemble cake, place a cooled layer on a serving plate. Spread 1/4 of filling evenly over top. Top with second layer, and spread with 1/3 of remaining apple mixture. Repeat with 2 more layers, dividing the remaining filling between them. Place final layer on top. Cover, and let sit overnight. Dust with confectioners' sugar just before serving.
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