Beat the egg yolks with the sugar and gradually add the oil, milk, vanilla and the mixed flour and baking powder, sifted beforehand.
Separately, beat the egg whites to snow, add them to the yolk mixture and stir with a spatula to a homogeneous mixture slowly and carefully.
Pour half the mixture into an oiled rectangular oven dish. To the other half, add the cocoa and stir. Pour the cocoa mixture over the white one and make a few streaks on it with a fork.
Put the oven dish in a preheated 356°F (180 °C) oven and bake until the cake is ready (check with a toothpick, it has to come out dry).
Sprinkle the cooled cake with powdered sugar, cut it into cubes and serve.