Wash and soak rice for 3 hours. Drain, spread in a white cotton cloth for 10 mins. Do not let it dry for long time as it will give rubbery adhirasam. Moisture should be there if you touch the rice.
Grind it in 2 batches in a mixer to a flour. Wipe down the sides to ensure even powdering.
Sieve it. My MIL and mom uses rava jalladai (sieve) for this, so I understand its important for the flour to be slightly on coarse side. While you sieve, keep the flour pressed and covered. That is after you sieve and transfer the flour to a narrow container, press it gently so that it locks the moisture and keep covered always so that flour doesn't get dried. Meanwhile, powder the jaggery and heat it with water just to immerse the jaggery.
Once its completely dissolved, filter it to remove impurities. Again start heating the jaggery syrup.
Boil in medium flame always and stir occasionally. Keep checking the syrup consistency by pouring in water kept in a small bowl. At beginning stage, the syrup dissolves as you pour in water, then at next stage, it will lay a fine thread in the water, but gets dissolved when you touch. After this, at one stage, the syrup gets thicker and when you pour in water, then it wont get dissolved and you will be able to gather it with your fingers and form a loose ball that stays in hand. This is called soft ball consistency and this is the stage, you have to put off the fire. Immediately pour it to the flour little by little. Add sesame seeds, cardamom powder and dry ginger powder to the flour.
You may need not all the sugar syrup for sure. So be careful after you add 3/4th of the syrup and keep mixing with a ladle or spatula. The syrup should be super hot directly used from stove. Mix well for atleast 3 mins. The dough should be gooey and on sticky side and it should be very very loose (pouring consistency). After some hours, it will get absorbed and get stiff.
Keep it overnight (2 days if possible, for better result) at room temperature in an airtight container. You can keep it as such for 2-3 days. If more than that, keep refrigerated. But let it be out overnight atleast for a day. At the time of making, divide into equal sized balls, each of small lemon sized. You can use sesame oil when you roll as the dough will be slightly sticky.
Heat oil in kadai and once it is hot, reduce the flame to low. In a ziploc, grease it with a drop of ghee and flatten the dough thick. Carefully drop in oil.
Once it rises up, immediately flip it and cook. Once it turns golden brown, drain from oil.
You must use another ladle and press it to squeeze out the excess oil as shown, as it may retain some oil in it. Repeat the process for the rest of the dough. Oil should always be in low or medium if needed.