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1
Preheat the oven to 350u00b0 F. Generously butter an 8-inch springform pan. Coat the bottom and sides of the pan with granulated sugar then tap out the excess. Set aside.
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2
Place the cider in a small saucepan and reduce by half over medium-high heat. Set aside to cool slightly, then stir in the maple syrup.
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3
While the cider is cooling, use a paring knife to halve the vanilla bean lengthwise. Scrape the seeds from the pod using the blade of the paring knife. Add the vanilla seeds to the sugar in a small bowl. Use your fingers to rub the vanilla seeds into the sugar. (This will keep the vanilla from clumping together in the batter.)
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4
Crack the eggs into a large bowl. Whisk until frothy then add the vanilla sugar. Continue to whisk until the eggs look frothy again and the sugar is starting to dissolve, a minute or so longer. Whisk in the cider-maple reduction then whisk in half the flour mixture. When the flour is just incorporated, add half the butter, then the rest of the flour mixture and then the rest of the butter, whisking after each addition until you have a smooth, fairly thick batter.
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5
Pour a little more than half the apples into the prepared cake pan. Pour the cake batter over the apples and smooth the top with a flexible spatula so no bits of apple are sticking up through the batter. Arrange the rest of the apples over the top of the batter in 1 or 2 slightly overlapping concentric circles. Sprinkle with 2 tablespoons of sugar, if desired, to make the top a bit more golden and crunchy.
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6
Bake the cake, rotating after 30 minutes, for 50-60 minutes total, until the top of the cake is golden brown, a toothpick inserted into the center comes out clean and the cake pulls away from the sides of the pan. Transfer to a cooling rack and let rest for 5 minutes. Carefully run a butter knife around the sides of the cake to loosen it from the pan, then unmold and cool completely on the wire rack before slicing.
