Beat the yolks with half the sugar to a fluffy cream. Add the 4 eggs 1 by 1 and continue beating with a mixer, while also adding the rest of the sugar in a thin trickle. Add the oil and stir. Add the flour in lots and stir carefully until you get a fluffy cake batter.
Beat the whites with a mixer in a bowl to a fluffy cream. Continue beating, while adding the sugar in lots. Once you get a thick cream, stop beating and carefully add the flour, stirring from the bottom up, while being careful not to deflate the mixture.
To the ground walnuts, add the cocoa and stir until homogeneous.
Butter a cake form and sprinkle lightly with flour.
Start assembling the cake as follows: pour on some of mixture 1 (the yellow one), then sprinkle a layer of walnuts and cocoa, put the egg white mixture, walnuts again and finish off with the yellow mixture.
Bake the cake in a preheated 356°F (180 °C).