Now the rice wouldn't be dripping but it still would be having moisture in it. This is the right time to get it powdered. So take the rice in a mixer and grind to fine powder. Sieve this rice flour and transfer it to a wide bowl.
Add sesame seeds and cardamom powder to the flour, mix and keep it covered, so that moisture isn't lost. Next heat a wok with jaggery and little water (around 1/4 cup). Cook till the jaggery dissolves completely.
Get the jaggery syrup filtered by pouring it through the fine strainer. This helps to remove the impurities. Next heat jaggery syrup in the same wok till syrup reaches soft ball consistency. Meaning when you pour a drop of syrup in some water, it should be firm such that you can make ball out of it.
Next add jaggery syrup in parts to the rice flour in the bowl. Keep mixing as you add the syrup. The rice flour would absorb the syrup and becomes gooey and loose. You don't require all jaggery syrup, so add as needed. Let this gooey dough rest in a container for about a day.
Next day you will find the dough stiff and sticky. Greasing some ghee to your palms, take lemon sized dough and pat it over a banana leaf like thick disc. Heat oil in heavy bottom pan and drop the disc in to oil. As it puffs up, turn to cook the other side.
When it turns brown, remove from oil and using one more spatula press to drain extra oil.
continue this process till you are done with all the dough. Adhirasam or kajjaya is ready to serve as Diwali sweet.