Use a whisk or handheld beater to cream the butter. Add the sugar and vanilla extract and beat until well incorporated.
Pour in the yogurt and mix to combine.
Sift in the flour and baking powder and mix until just combined.
Add the milk and use a whisk or handheld beater to beat for a minute.
Pour the mixture into a microwave-safe dish lined with parchment paper. Bake in the microwave for between 6 to 8 minutes or the high power setting.
Check if the cake is baked after 6 minutes by inserting a toothpick in the centre. The cake should be baked if the toothpick comes out clean.
If after 6 minutes the cake has not finished baking, continue to bake it until done.
Keep in mind that the cooking time is going to vary depending on your microwave and the container you are using.
After baking, allow the cake to cool in its container for 10 minutes. Then gently remove it from the container onto a plate. Cool completely before decorating with a frosting of your choice.