Preheat the oven to 180°C (350°F), medium temperature. Grease two 9x13 rectangular baking pans with butter. Cut two parchment paper rectangles to fit the pan bottoms. Press the parchment into the pans, grease the paper with butter, and dust lightly with flour. Shake to distribute evenly and tap out any excess.
Prepare the ingredients: Sift the sugar into a bowl to ensure there are no lumps. In another bowl, mix the ground walnuts with the breadcrumbs and set aside.
Separate the eggs: Break one egg at a time into a small bowl, transferring the whites to the mixing bowl and the yolks to another bowl.
Whip the egg whites: Using a stand mixer, beat the egg whites on low speed until foamy. Gradually increase to high speed and beat for about 5 minutes until stiff peaks form.
Incorporate the yolks and sugar: Add the egg yolks one at a time, beating well after each addition. Gradually add the sugar, continuing to beat until you achieve a light, fluffy, and shiny mixture. Pause as needed to scrape down the sides of the bowl with a spatula to ensure all the sugar is well incorporated.
Fold in the dry ingredients: Transfer the egg mixture to a large bowl (it needs to be large enough to mix all the batter). Gently fold in the walnut and breadcrumb mixture a little at a time, using a spatula and mixing from the bottom up to avoid deflating the batter.
Divide and bake: Divide the batter evenly between the prepared pans and level the surface with a spatula. Bake for about 30 minutes or until a toothpick inserted into the center comes out clean.
Cool before unmolding: Remove the cakes from the oven and allow them to cool completely before removing them from the pans. Meanwhile, prepare the filling.