Preheat the oven to 350° with a rack in center. Prepare a 13 x 9 pan with non-stick baking spray.
Beat the butter, oil, sugar, and eggs together with an electric mixer for 3-5 minutes in a large mixing bowl, until fluffy and lightened in color. Add the molasses and boiled cider and mix.
Combine the dry ingredients (flour, ginger, cinnamon, cloves, allspice, salt, baking powder, and baking soda) in a separate large mixing bowl and mix until combined. Add the dry ingredients to the wet ingredients and stir by hand or with the mixer on low until just combined. Don't overmix.
Add the grated apple and sourdough starter to the batter and mix by hand until they are evenly distributed throughout the batter. Pour the batter into the prepared pan.
Bake for 45 minutes, until a toothpick inserted into the center of the cake comes out clean, or with just a few moist crumbs. Place pan on cooling rack and allow the cake to cool to room temperature in the pan, for at least an hour.