Traditional Polish Apple Cake (Szarlotka)

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1. 1Step 1: Core, peel and cube the apples and place in a large pot along with the lemon juice, cinnamon and 2.5 tablespoons of sugar. Stir thoroughly, cover and cook over medium heat for about 10 minutes or until the apples have released their juices and softened, stirring gently occasionally.
2. 2Step 2: Remove the lid and continue cooking for 3-4 more minutes, stirring gently. Remove from the heat and set aside to cool completely, stirring once in a while (the apples will absorb excess moisture as they cool).
3. 3Step 3: While the apples are cooling, prepare the dough. Place the flour, baking powder, salt, sugar, 4 egg yolks, butter, vanilla extract and yogurt in a food processor. Pulse until the ingredients come together in a dough.
4. 4Step 4: Place the dough on a flat surface and form a log. Cut it into 2 parts (2/3 and 1/3). Place both on a plate or cutting board and freeze for 30 minutes.
5. 5Step 5: After about 20 minutes, preheat the oven to 375 F / 190 C / gas mark 5. Lightly grease a 23/33 cm (9/13 inch) pan and dust with flour (or line with parchment) and set aside.
6. 6Step 6: Remove the dough from the freezer (place the smaller piece in the fridge for now). Cut the larger dough into thin slices (approx. 5mm thick) and arrange in a single layer in the bottom of the baking pan. If you don't have enough slices, you can cut a little off the smaller dough and use that.
7. 7Step 7: Press down with your knuckles to spread the dough evenly over the bottom of the pan. Place the pan in the fridge while you prepare the egg whites.
8. 8Step 8: Beat the egg whites with a pinch of salt until soft peaks appear, then gradually add 2.5 tablespoons of sugar, beating all the time until the mixture is thick and firm. Set aside.
9. 9Step 9: Remove the pan as well as the remaining dough from the fridge. Spread the apple filling (it should be completely cooled by now) over the layer of dough and even out without pressing down too much.
10. 10Step 10: Spread the egg white mixture over the top.
11. 11Step 11: Coarsely grate the remaining dough over the whole thing without pressing down.
12. 12Step 12: Bake in the centre of the oven for 40 minutes, then cover loosely if necessary (to prevent the top becoming too dark) and continue baking for another 25 minutes (to ensure the bottom of the cake is fully cooked).
13. 13Step 13: Remove from the oven and set aside to cool before cutting. Dust your apple cake with a little icing/powdered sugar before serving.