Beat the egg yolks with half the sugar until you get a smooth cream and with the remaining sugar, beat the egg whites into hard snow. Add oil, milk and gradually the flour and baking powder to the yolks. Then mix them with the vanilla, rum and rum essence.
In batches, add the egg whites and stir gently with a spatula. Divide the mixture into 2 parts and mix one with the cocoa. Grease and lightly flour a cake form. Begin alternating between equal parts of the white and brown mix, spoon by spoon, in the center of the form. Keep alternating until you have used up the mixtures.
Put the cake to bake in a preheated 356°F (180 °C) oven for about 50 minutes. At the end, check to see if it is ready with a wooden stick. Optionally, you can smear the finished cake with a little rum, mixed with powdered sugar, by using a brush, or just sprinkle it with powdered sugar.