Combine the apples in a large Dutch oven with the brown sugar, cinnamon, ginger, and nutmeg, stirring gently so the spices coat every piece. Add enough water to cover the apples, then cook down until soft and spreadable.
Preheat the oven to 350°F (175°C). Coat two or more 9-inch cake pans, or a 9 1/2-inch cast iron skillet, with cooking spray.
Beat the shortening, sugar, and molasses together until smooth, then work in the eggs, buttermilk, and the combined flour, baking soda, baking powder, and salt to form the stiff dough.
Press or spread a thin portion of dough into each pan. Bake about 15 minutes, until the layer is firm when lightly pressed; it will not rise as it bakes, so a flat, biscuit-like round is correct, not a fault.
Turn the first layer out onto a cake plate as soon as it leaves the oven and spread 1 cup of the apple mixture over it. Add the next layer, spread another cup of apples, and repeat through all layers.
Cover the assembled cake with plastic wrap or an airtight container and let it sit at room temperature for 2 days, so the layers absorb the apple mixture.