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1. Adjust oven rack to lower-middle position and heat oven to 325 degrees. Spray 9-inch springform pan with vegetable oil spray. Place prepared pan on rimmed baking sheet lined with aluminum foil. Place apple slices into microwave-safe pie plate, cover, and microwave until apples are pliable and slightly translucent, about 3 minutes. Toss apple slices with Calvados and lemon juice and let cool for 15 minutes.
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2. Whisk 1 cup flour, 1 cup granulated sugar, baking powder, and salt together in bowl. Whisk egg, oil, milk, and vanilla together in second bowl until smooth. Add dry ingredients to wet ingredients and whisk until just combined. Transfer 1 cup batter to separate bowl and set aside.
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3. Add egg yolks to remaining batter and whisk to combine. Using spatula, gently fold in cooled apples. Transfer batter to prepared pan; using offset spatula, spread batter evenly to pan edges, gently pressing on apples to create even, compact layer, and smooth surface.
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4. Whisk remaining 2 tablespoons flour into reserved batter. Pour over batter in pan and spread batter evenly to pan edges and smooth surface. Sprinkle remaining 1 tablespoon granulated sugar evenly over cake.
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5. Bake until center of cake is set, toothpick inserted in center comes out clean, and top is golden brown, about 1 1/4 hours. Transfer pan to wire rack; let cool for 5 minutes. Run paring knife around sides of pan and let cool completely, 2 to 3 hours. Dust lightly with confectioners' sugar, cut into wedges, and serve.
