Grease a 23-centimeter round cake pan and line with bakery paper. Greasing the edges of the pan is unnecessary.
Preheat the oven for 15 minutes at 180 degrees.
Sift the flour and baking powder together 3 times to ensure that the flour particles are well-separated and light.
Beat the eggs, sugar, and vanilla with a mixer. Stir them for about 4 o 5 minutes until they double in volume.
Reduce the speed of the mixer and add liquid oil. Do not pour the oil into the middle of the dish. Rather, add it from the corners of the dish.
Add milk and stir the mixture until combined. Do not over-mix. Then turn off the mixer and set it aside.
Using the sifter, gradually add the flour in 2 to 3 batches, and stir it with a silicone spatula or whisk to combine.
Divide the cake batter into 2 equal portions, add 2 tablespoons of cocoa powder to one part and 2 tablespoons of flour to the other part.
Working from the center of the dish, pour some white batter into the cake pan first, then some cocoa batter over that. To achieve a zebra cake pattern, alternate between white and cocoa batters until all the batter has been used. For a simple zebra cake, we said that alternating 4 layers of white and cocoa batter is sufficient.
Finally, to make your cake more attractive, pour cocoa batter in the middle of the cake.
Bake the cake at 180 degrees for 50 to 60 minutes, until you can pierce its center with a toothpick, and it comes out clean.