Pressure cook 1/2 cup rice in 1 cup of water until soft ( in case using the stove top to cook rice use water as needed until the rice is soft ). Dry roast brown sesame seeds until they turn darker and keep aside. When cooled, grind the sesame seeds into a coarse powder.
In a large heavy bottom pan, place the grated jaggery with 1/4 cup water and heat.
In a cup nearby, keep about 1/2 cup of cold water handy.
When the jaggery starts boiling and starts thickening take half a tsp of the boiling jaggery and pour into the 1/2 cup of cold water nearby. If the jaggery spreads and mixes with the water then it is not done.
If the jaggery stays firm and you are able to roll the jaggery between your fingertips, then it is ready.
At this point, lower the heat and add the cooked rice to the jaggery mixture and mix well. Add the sesame seed powder to this.
Add clarified butter, cardamom powder to this mixture and keep stirring it on low heat.
When the entire mixture starts thickening and the sides start leaving the pan, it is done. Turn off the heat and serve hot.