1. Preheat the oven to 180°C (350°F).
2. In a bowl, mix together the yogurt, flour, baking powder, sugar, oil, and eggs.
3. Divide the batter into 2 parts: in the first batter, add the vanilla extract, then in the second batter, add the cocoa powder.
4. In a greased and floured cake pan, place 1 tablespoon of plain batter in the center, then 1 tablespoon of chocolate batter on top and in the center of the vanilla batter. Repeat the process until there is no more batter. By layering the batter on top of each other, the cake batter will spread as it bakes.
5. Bake for 25 to 30 minutes.