Preheat the oven to 180 °C (350 °F) and grease a Bundt pan.
Whisk the eggs with the sugar and vanilla until the mixture triples in volume and becomes foamy.
Add the oil while continuing to whisk, then incorporate the yogurts and mix well to obtain a smooth batter.
Add the baking powder, mix, then incorporate 300 g (10.6 oz) of sifted flour and mix again.
Divide the batter into two equal parts in two mixing bowls. In one bowl, add 30 g (1 oz) of flour and mix. In the other, add the cocoa and mix well.
Pour half of the plain batter into the mold, then half of the cocoa batter. Cover with the remaining plain batter, then finish with the remaining cocoa batter to create beautiful marbled swirls.
Bake for 35 to 45 minutes. Check for doneness by inserting a skewer into the center of the cake: it should come out clean.
Unmold the cake by turning it onto a wire rack and let it cool completely before slicing.