Put the dried apples, light brown sugar, cinnamon, ginger, nutmeg, and 4 cups water in a large pot. Ensure the apples are covered, then bring the mixture to a boil over high heat. Lower the heat and let it simmer gently for about 1 hour, stirring often to prevent scorching.

If the filling becomes too thick or dry, add up to 1 more cup of water as needed.

When the apples are soft, remove the pot from heat. Use a potato masher to turn the mixture into a chunky sauce, letting it cool completely before use.

Preheat the oven to 350°F and coat two 9-inch cake pans with baking spray.

In one bowl, whisk together the flour, baking powder, baking soda, and salt.

In another bowl, beat the shortening with granulated sugar for 2 to 3 minutes until fluffy. Beat in the molasses, vanilla, and dark brown sugar until smooth, adding the eggs one at a time while scraping down the bowl as needed.

Add the flour mixture in three additions, alternating with the buttermilk, mixing only until combined. Spread about one sixth of the batter into each prepared pan and bake for 14 to 18 minutes, until set and lightly browned. Repeat until all layers are baked.

While each layer is still warm, place it on a large cake plate and spread about 1 cup of the apple filling over it. Stack the layers, leaving the top layer bare, and let it sit in an airtight container at room temperature for 2 days for the layers to absorb moisture.

Slice and serve after resting.