1 tablespoon Calvados (apple brandy or white rum)
1 teaspoon lemon juice
1 cup + 2 tablespoons all-purpose flour (divided)
1 cup + 1 tablespoon granulated sugar (divided)
2 teaspoons baking powder
½ teaspoon salt
1 egg
2 egg yolks
1 cup vegetable oil
1 cup whole milk
1 teaspoon vanilla extract
Powdered sugar (for dusting)
Adjust oven rack to lower-middle position and preheat oven to 325 degrees F. Spray a 9-inch springform pan with non-stick cooking spray. Place the prepared pan on a rimmed baking sheet lined with aluminum foil. Place the apple slices into pie plate, cover with an inverted plate, and microwave until the apples are pliable and slightly translucent, about 3 minutes. Toss the apple slices with Calvados and lemon juice and let cool for 15 minutes. In a medium bowl, whisk together 1 cup of the flour, 1 cup of the granulated sugar, baking powder, and salt. In a large bowl, whisk together the whole egg, oil, milk, and vanilla extract until smooth. Add the dry ingredients and whisk until just combined. Transfer 1 cup of the batter to a separate small bowl and set aside. Add the egg yolks to the remaining batter in the large bowl and whisk to combine. Using a rubber spatula, gently fold in the cooled apples. Transfer the batter to the prepared pan; using an offset spatula, spread the batter evenly to the pan edges, gently pressing on the apples to create even, compact layer, and smooth surface. Whisk the remaining 2 tablespoons of flour into the reserved batter. Pour over the batter in the pan and spread evenly to the pan edges and smooth the surface. Sprinkle the remaining 1 tablespoon granulated sugar evenly over the cake. Bake until the center of the cake is set, a toothpick inserted in the center comes out clean and the top is golden brown, about 1 hour 15 minutes. Transfer the pan to a wire rack and cool for 5 minutes. Run a paring knife around the sides of the pan and cool completely, 2 to 3 hours. Dust lightly with powdered sugar before serving.