Coarsely grind the rice and coconut in your blender.
Mix the water, jaggery, cinnamon and cardamom and bring to boil, till the jaggery is melted. Add the coarsely ground rice mixture and give it a nice stir. Add in the salt and the plantain.
Cook till the mixture starts to thicken, around 5 minutes. Check for the sweetness and adjust the salt levels.
Add water to slightly loosen the mixture. Serve warm.
The payasam thickens when kept and therefore, just before serving, add some warm water and give it a nice mix.
The taste of this payasam is primarily the cinnamon, and also gives the sourness of the cooked plantain. You may replace the plaintain with some cooked chana dal as well, which is another variation.