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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.
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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.
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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.
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Prepare the topping by heating the butter, sugar, boiled cider, cinnamon, and corn syrup together over low heat, stirring until the sugar is dissolved.
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Pour 1/2 cup of the syrup mixture into the prepared pan, and set the rest aside.
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To make the cake: Beat the oil, brown sugar, boiled cider, eggs, spices, and salt together for 2 minutes at medium speed
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Mix the flour with the baking soda, and stir it into the batter.
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Add the chopped apple and nuts, and mix until just blended.
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Drop scoops of the batter atop the apples in the pan, gently spreading to cover.
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Bake the cake for 50 to 55 minutes, or until a cake tester inserted near the center comes out clean.
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Remove the cake from the oven, and run a thin spatula around the edge to loosen.
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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.
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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.
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Pour the sauce over the cake. Serve cake warm or at room temperature, with whipped cream if desired.