Place the oven rack to the lower-middle position and heat the oven to 325 degrees.
Spray a 9-inch springform pan with vegetable oil spray and place it on a baking sheet covered with aluminum foil.
Place apples into a pie plate, cover them with a dinner plate, and microwave for 3 minutes until apples start to soften and they are slightly translucent. Add Calvados (if using) and lemon juice. Give it a big toss. Set aside for it to cool.
In a large glass bowl, whisk 1-cup flour, 1-cup sugar, baking powder, and salt. In a second glass bowl, whisk 1 egg, oil, milk, and vanilla until it is smooth.
In two batches, add the dry ingredients to the wet ingredients and whisk just until combined.
Measure 1 cup of this batter and set it aside.
Add the egg yolks to the remaining batter (the larger batch) and whisk to combine.
With the help of a spatula, gently fold in the apples into the batter. The apples should be much cooler at the point.
Transfer the batter into the 9-inch springform pan. Using a spatula spread the batter evenly.
Whisk in the remaining 2 tablespoons of flour into reserved 1-cup batter and mix until combined. Pour it over batter in the pan and spread it evenly to the edges of the pan. Sprinkle the remaining 1-tablespoon sugar over the batter.
Place in the oven and bake it for 1 hour and 15 minutes or until a toothpick inserted into it comes out clean and the top is golden brown. Be sure to keep an eye on it after the 1-hour mark. You want the top of the cake to be golden brown.
Place it on a wire rack and allow it to cool for at least an hour. Dust it with confectioners’ sugar and serve.