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 about 1/2 cup of the syrup mixture into the prepared pan, and set the rest aside.
To make the cake: In the bowl of a stand mixer fitted with the flat beater attachment or working in a large bowl with an electric hand mixer, beat the oil, brown sugar, boiled cider, eggs, spices, and salt together for 2 minutes at medium speed.
Add the flour and the baking soda, then stir until well combined.
Add the chopped apple and nuts, and mix until just blended.
Carefully transfer the batter to the pan, covering the apples but not disturbing them. Smooth the top of the batter.
Bake the cake for 50 to 55 minutes, or until a toothpick or paring knife 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 the Apple Upside-Down Cake warm or at room temperature, with whipped cream if desired.
Storage information: Leftover Apple Upside-Down Cake can be stored airtight in the refrigerator for up to 1 week. Remove and warm in a 350°F oven for 10 minutes before serving.
