Preheat the oven to 350 deg F. Grease a cake pan, line it with parchment paper and set aside.
Add the yogurt and sugar to a wide bowl and whisk them together. Make sure the sugar is dissolved completely.
Now add the baking powder, baking soda, and salt. Mix them and let them sit for 5 minutes.
The mixture will be emulsified now.
Add the vanilla extract and whisk again. Now slowly pour the oil and whisk the mixture. This helps in excellent emulsification.
Sieve the all-purpose flour into this wet mix and combine gently.
Make sure there aren't any lumps.
Pour this cake batter into the cake pan and spread it evenly.
Tap it twice so that the mixture settles. Bake the cake for about 40 to 45 minutes or until a toothpick inserted in a center comes out clean. Let it cool for 15 min. And slowly remove the cake from the pan. Let it cool for atleast one hour before adding the frosting.
Every oven is different, and timing might differ between convection and conventional oven, the rack position, etc. Make sure you bake until when a toothpick inserted in a center comes out clean. For this measure, you might not need to bake beyond 45 minutes.
Please check the other variations that I mentioned in the post.
The frosting is optional. If I am making for a party, I usually do the frosting.