Adjust an oven rack to the lower-middle position and heat the oven to 325 degrees F. Spray a 9-inch springform pan with non-stick spray. Place prepared pan on a rimmed baking sheet lined with aluminum foil.
Place apple slices into a 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.
Whisk 1 cup flour, 1 cup granulated sugar, baking powder, and salt together in a bowl. Whisk egg, oil, milk, and vanilla together in a second bowl until smooth. Add dry ingredients to wet ingredients and whisk until just combined. Transfer 1 cup batter to a separate bowl and set aside (this will become the cake layer).
Add the egg yolks to the remaining batter (to create the custard layer) and whisk until just combined. Using spatula, gently fold in cooled apples.
Transfer custard/apple batter to prepared pan and, using an offset spatula, spread the batter evenly to the pan edges, gently pressing on the apples to create an even, compact layer, and smooth surface.
Whisk the remaining 2 tablespoons flour into the reserved batter. Carefully and evenly pour this batter in the pan on top of the custard/apple layer. Spread the batter 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 1/4 hours.
Transfer pan to a wire rack; let cool for 5 minutes. Run a paring knife around the sides of the pan to dislodge the cake and then let cool completely, 2 to 3 hours. Dust lightly with confectioners' sugar if desired, cut into wedges, and serve. For a nice crisp top, serve the same day without covering the cake. I loosely covered the remaining cake with foil overnight, and the crispness was lost due to the moisture of the cake (it's still good though!)