Preheat your oven to 350°F (175°C) and grease a round cake pan.
In a large bowl, mix yogurt and sugar until well combined.
Add the eggs one at a time, mixing thoroughly after each addition.
Stir in the vegetable oil and vanilla extract.
In a separate bowl, whisk together flour, baking powder, and salt.
Gradually add the dry ingredients to the wet mixture, stirring until just combined.
If desired, fold in lemon zest for added flavor.
Pour the batter into the prepared cake pan.
Bake for 30-35 minutes or until a toothpick inserted in the center comes out clean.
Allow the cake to cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.