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.
Storage: The cake can be kept in an airtight container at room temperature for up to 2 days or in the refrigerator for up to 5 days.
Make-Ahead: The cake needs to be cooled for 2 to 3 hours to allow it to set before serving. This makes it a perfect candidate to be baked in the morning and served in the evening. You can even prepare it up to 24 hours in advance and keep at room temperature until serving.
Freezing: Allow the cake to cool completely, then wrap in two layers of plastic wrap and a layer of aluminum foil. Freeze for up to 3 months. Thaw at room temperature overnight before serving.