Whisk the eggs and sugar together for few minutes, then add the oil and whisk for few more minutes until little frothy.
Then add the yoghurt, vanilla extract and whisk again.
Now sieve in the flour & baking powder into the batter. Mix it using cut and fold method.
Pour this mixture into a greased cake tin. Smoothen the top with a spoon.
Cut the plums into quarters. Arrange them on top of the cake. Sprinkle brown sugar on each plum.
Bake this for 45-50 minutes in a preheated oven at 170 degree Celsius. Cool and serve.