Preheat oven to 180 degrees C (350 degrees F).
Line a 18-20 cm cake pan (7-8 inch) with a circle of baking paper.
Divide the eggs placing the whites in one large bowl and the yolks into another.
Beat the yolks together with the sugar until the mixture becomes thick and creamy. Add yogurt, vanilla and olive oil and beat few more minutes, until combined. Gradually add the flour, mixing gently with a rubber spatula.
In another bowl beat the egg whites until soft peaks form. With the rubber spatula gently fold the whites into the yolk mixture.
Transfer the batter into the prepared pan and bake for about 40 minutes or until a wooden skewer inserted in the centre comes out clean.
Remove from the pan and let cool until room temperature before assembling the cake.