Preheat oven to 350°F. and place rack in the middle position.
To make cake:
Combine the dry ingredients in a bowl and whisk to combine. Set aside. Combine the butter and 1-1/4 cups sugar in the bowl of a standing mixer fitted with paddle attachment and mix on medium speed until wet and grainy. Add the sorghum syrup or molasses. Scrape the sides of the bowl with a flexible spatula to get all of the syrup into the mixture.
Add the eggs 1 at a time. Scrape all the way to the bottom of the bowl and mix on low speed. Alternately add the buttermilk and the dry mixture about a quarter at a time. Stop the mixer to scrape the bowl, then mix on low speed for about 10 seconds. The mixture should be stiff like a soft cookie dough. Shape the dough into a ball and wrap it in plastic wrap. Refrigerate for 30 minutes.
Divide the dough into 6 or 8 equal portions and place each one on a round piece of parchment paper a little larger than a 9-inch cast-iron skillet. Roll out the dough to the size of the parchment. Leaving the parchment paper underneath, lift the disks onto baking sheets and bake them for approximately 10 minutes, or until the top surface appears dry and a wooden skewer inserted in the center comes out clean. Slide the disks off the baking sheet onto a flat surface to cool.
To make apple filling:
Combine all the ingredients in a large, heavy-bottom saucepan and bring to a light simmer. Immediately transfer to the work bowl of a food processor fitted with the steel blade and pulse into a thick paste.
To assemble the cake, spread about 1 cup of the filling onto each layer, taking care to center each disk on top of the one beneath it. Repeat until all the layers are used. Spread filling around sides of cake. Do not put apple filling on top of the cake. Wrap the cake well and refrigerate it for up to 24 hours. This gives the apple filling time to work itself into the cake. Dust with powdered sugar and serve chilled.