Mix the flour, sugar and salt in a large bowl. Toss the butter cubes until fully coated. Use a pastry blender to cut in the butter until mixture reassembles a coarse meal.
In the small bowl mix together water and yolks.
Add water mix to the flour mixture and stir with fork until a soft dough ball is formed. You will need help of your hands at some point but try to minimize contact with the dough. Add little more water if necessary.
Divide the dough ball into four equal portions. From each portion create a 130 mm x 100 mm (5″ x 4″) rectangle. Wrap each portion in a plastic wrap and refrigerate about 1-2 hours. Shaping in a rectangle will help you later with rolling the dough out.
Apple Filling
Cut into 6 mm (1/4″) slices about 60% of the total number of apples. For example if you had 6 apples, slice 4 of them. Slice on all sides till you get to the core.
Grate the reminder of apples on the large holes of a box grater.
Combine the sliced and grated apples, honey, lemon juice, and cinnamon in a large sauce pan. Cover the pan and place over medium low heat. Heat until apples give off some juices. Uncover and cook until sliced apples become tender, about 8-10 minutes. Stir occasionally. Transfer to a bowl and cool completely.
Walnut Filling
Process the walnuts and sugar in a food processor until nuts are chopped finely.
Put the walnut/sugar mix together with water into a medium size saucepan. Stirring constantly, bring the mixture to boil over medium heat. Continue cooking until a thickened, moist paste is formed, approximately 3 minutes. Don’t make it too thick. When cooled off it will become hard and unworkable. Transfer to a new bowl to avoid overcooking and let cool.
Poppy Filling
Grind the poppy seeds in small 1/4 cup batches using coffee grinder.
Into a small size saucepan, add together poppy seeds, sugar, and water. Stir constantly, cooking over medium heat until the water is absorbed and the mixture has thickened into a moist paste, approximately 2 minutes. Transfer to a bowl and let cool.
Assembly
Preheat the oven to 205 °C (400 °F) with a rack positioned in the middle of the oven.
Butter the inside of 30 cm x 20 cm (11 1/2″ x 8″) baking dish with toll sides.
On a lightly floured work surface, roll out the first dough portion into a 30 cm x 20 cm (11 1/2″ x 8″) rectangle. Transfer to the baking dish and spread evenly with the apple filling.
Roll out the second dough portion into a 30 cm x 20 cm rectangle and place over the apple filling, pressing lightly to make it as flat as possible. Spread the walnut filling on top.
Roll out the third dough portion into a 30 cm x 20 cm rectangle and fit over the walnut filling, press lightly. Spread the poppy seed filling.
Roll out the third dough portion into a 30 cm x 20 cm rectangle and fit over the poppy seeds filling, press lightly. Pierce the top dough all over with a fork.
Beat the egg yolk and cream in a small bowl and brush over the top dough.
Put the cake in the oven and bake for 10 minutes on 205°C (400°F). Reduce the oven temperature to 175 °C (350 °F) and bake until the top is golden brown, about 50 minutes.
Transfer to a wire rack and cool in the baking dish for about 15 minutes. Run the sharp knife around the edge, inside the dish. Place a baking sheet over the top and unmold the cake by inverting it. Now place the cooling rack over the cake and invert it back to right side up. Cool completely, at least 2 hours and ideally wrap in plastic wrap and let it sit overnight.
Using a serrated knife trim off the edges. Cut the dessert into 12 bars and serve at the room temperature.