In a large bowl add yogurt and beat the yogurt with a whisk to remove any lumps. Add baking soda and mix it well. Set a side for 5-7 minutes, not more than that.
In a large bowl add oil and sugar and whisk for two minutes.
After five minutes, you will see small bubbles in the yogurt mixture. Add the yogurt mixture and vanilla extract to the sugar mixture and mix well.
Sieve the flour and baking powder and add the sieved flour in two batches and fold in gently to remove any lumps. Do not over mix.
Transfer the batter to the prepared baking dish. Bake the cake for 30 -35 minutes until the tooth pick inserted comes out clean. Mine was done by 30 minutes. The time may vary depending on the oven and size of the pan.
Let the cake cool for 10 minutes, not more than that.