Preheat oven to 325° F. Spray 9-inch springform pan with vegetable oil spray; line with parchment paper. Place prepared pan on aluminum foil-lined rimmed baking sheet. Set aside.
Place apples in pie plate, cover, and microwave until apples are pliable and slightly translucent, about 3 minutes. Toss apples 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 small bowl. Whisk oil, milk, egg, and vanilla in larger bowl until smooth. Add flour mixture to milk mixture and whisk until just combined. Transfer 1 cup batter to separate bowl and set aside.
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.
Whisk remaining 2 Tablespoons flour into reserved batter. Pour over batter in pan, spread batter evenly to pan edges, and smooth surface. Sprinkle remaining 1 Tablespoon granulated sugar evenly over cake. Bake until center of cake is set, toothpick inserted in center comes out clean, and top is golden brown, about 1 hour and 15 minutes. Let cake cool in pan on wire rack for 5 minutes. Run think knife around pan to loosen cake, and let cool completely, 2 to 3 hours. Remove sides of pan. If desired, dust cake likely with confectioners’ sugar, and cut into wedges. Serve. Yield: 9-inch cake.