Preheat the oven to 175℃ (350℉).
Grease two 8" / 20cm pans and line the bottoms with baking paper.
In a large mixing bowl (or the bowl of a food processor) beat the eggs and sugar together for around five minutes.
In a separate bowl, whisk together the flour, baking soda, baking powder, and salt.
In a third bowl, combine the olive oil, milk, Greek yoghurt and vanilla essence.
With the mixer/processor on low speed, alternate adding the dry and wet ingredients (starting with dry). Do this in three stages, so add around a third of the dry ingredients, followed by a third of the wet. Repeat until you've added everything.
Divide the batter between the two cake pans.
Bake for 25 to 30 minutes or until a toothpick comes out clean. Remove from the oven.
Leave the cakes in the pans for around ten minutes, then turn out onto a wire rack and allow to cool completely.