Preheat the oven to 350 F.
Grease a 9"x9" baking pan with lemon olive oil. In a large bowl combine the sugar, eggs, yogurt, vanilla, and lemon olive oil. Whisk until pale and well combined. Whisk the dry ingredients together and add to the wet ingredients.
Pour into the prepared pan and bake for 25-30 minutes in the center of the oven until golden brown, or until a toothpick inserted into the center comes out clean.
Cool for 15 minutes in the pan, and invert on to a rack and cool fully before serving.