Stir the eggs and sugar until you get a homogeneous mixture. Add the oil, continue stirring, then add the vanilla.
Put the baking powder in the flour, sift and add these to the mixture. Pour it out into a suitable form with a little oil. Optionally, set aside 1/3 of the mixture and add the cocoa to it.
Stir well and add the cocoa mixture to the other one. Bake at 338°F (170 °C), cover with foil if needed, in order to bake well inside and prevent burning on the top.
Once the cake is ready, cover it with a cotton towel until it cools, to make it easier to remove from the form. Optionally, decorate with powdered sugar, cream or chocolate spread.