In a bowl, combine all the wet ingredients along with the grated carrots. Make sure that you grate the carrots really fine as we are going to use the microwave to bake them quickly. Large chunks of carrot might taste very raw.
In another bowl, combine all the dry ingredients. Mix them to combine using a wire whisk.
Add the wet ingredients to the dry and mix gently to combine. Do not over mix as the cake will turn our hard.
Grease a couple of ramekins well with butter. Add the prepared batter to the bowl. Make sure that you fill it less than half way through as it will rise during cooking in the microwave. My ramekins were quite small and it was scary to watch them when cooking as I was constantly worried that they would spill out.
Microwave for a minute in 50% Power. The batter did rise quite a bit, so make sure that you are cooking it in low power. After a minute, cook it further for about 15 more seconds in full power to complete the baking.
Remove the ramekins from the microwave and set it to cool. Remember that the bowls will be quite hot to handle. So remove it carefully.
Once they cool down, run a knife along the edges of the bowl and remove the cake. Slice the cake in between and spread the cream cheese frosting in between the layers. Spread some frosting on the top as well and serve.