To make the topping: Preheat the oven to 350°F. Lightly grease a 9" round cake pan at least 2" deep. Line the bottom with parchment, and grease the parchment., Slice the top, including the stem, off one of the apples and set it aside before peeling and slicing the rest of the apples into 1/4" thick wedges., Place the apple top, stem side down, in the middle of the pan, and overlap the rest of the apple wedges in a ring around it., Prepare the topping by heating the butter, sugar, boiled cider, cinnamon, and corn syrup together over low heat, stirring until the sugar is dissolved., Pour 1/2 cup of the syrup mixture into the prepared pan, and set the rest aside., To make the cake: Beat the oil, brown sugar, boiled cider, eggs, spices, and salt together for 2 minutes at medium speed, Mix the flour with the baking soda, and stir it into the batter., Add the chopped apple and nuts, and mix until just blended., Drop scoops of the batter atop the apples in the pan, gently spreading to cover., Bake the cake for 50 to 55 minutes, or until a cake tester inserted near the center comes out clean., Remove the cake from the oven, and run a thin spatula around the edge to loosen., Let the cake cool in the pan for 5 minutes, then turn it out onto a serving plate, bottom side up. Scrape out any sauce that remains in the pan, and spread it over the cake., Reheat the reserved topping. If butter starts to separate as you reheat, add water by the teaspoon and stir until the butter rejoins the rest of the sauce., Pour the sauce over the cake. Serve cake warm or at room temperature, with whipped cream if desired.