Preheat your fan-forced oven to 350°F / 180°C (fan forced). Grease and line a 9in / 23cm springform or ring tin.
Pour the plain yogurt into a large mixing bowl. Add the eggs, sugar, vanilla paste, and oil, then whisk until everything is well combined. Add the flour and baking powder to the bowl and mix thoroughly until smooth.
Pour the batter into the prepared tin and bake for 30-40 minutes, or until a skewer inserted into the centre comes out clean.
Let the cake cool in the tin for 5 minutes before transferring it to a serving platter.
