Preheat the oven to 180 C / Gas 4. Lightly grease a deep baking tray.
Weigh the four eggs and record the weight. Measure out the butter to equal that of the four eggs, repeat with the sugar. Weigh two separate amounts of flour, one equalling the weight of two of the eggs and a second amount equalling the weight of one of the eggs. Measure out enough cocoa powder to equal the weight of one of the eggs.
Cream the butter and sugar together in a mixing bowl until light and fluffy. Divide the mixture in two.
Into batch 1, mix in two of the eggs followed by 1 teaspoon vanilla and mix until pale and creamy. Mix in the flour equalling the weight of two eggs, then stir through 2 dessert spoons of yoghurt. Spoon the mixture in dollops around the prepared baking tray.
Into the second batch of butter and sugar, mix in the remaining two eggs until pale and creamy. Add the remaining vanilla then fold in the flour equalling the weight of 1 egg and the cocoa powder. Mix in the remaining yoghurt then spoon in dollops around the plain cake mixture in the baking tray. Swirl the mixture around in the baking tray to partially combine, leaving clear swirls of each mixture.
Bake in the oven for about 45 minutes, until a skewer inserted into the centre comes out clean. Remove from the oven.
Allow to cool on rack before cutting into squares and enjoying.
Family loved it served warm, reminded them of fondant sponge in taste.