Peel and grate apples. Squeeze them in batches to get the juice out, and then transfer to a medium sized bowl. Grind walnuts.
In a large bowl, combine egg yolks and sugar. Mix with a hand mixer until completely integrated. Add lemon zest and mix again. At this point turn off hand mixer, take up a wooden spatula and start adding in flour and baking soda to the mix while integrating everything together. When it toughens, sprinkle some flour on your working area, and transfer the dough onto it. Work your dough, and add the butter in until you get a smooth, tough but soft mass. Divide into two parts.
Take the first half of your dough and roll it out with a rolling pin until it fits the bottom of your baking pan (approximately 8.5inches x 12 inches in size). Sprinkle the pan with a little bit of flour, and transfer the dough into it. Spread grated apples over the dough evenly.
Make the filling by mixing egg whites until stiff. Add sugar, ground walnuts, marmalade, and vanilla extract. Continue mixing until integrated. When done, pour evenly over grated apples.
Heat oven to 350°F. Take the other half of your dough and grate over your cake. Place the baking pan in the oven and bake for 50 minutes. Turn around about half-way through. If it starts blushing, cover with foil and add a little bit of baking time at the end.