For homemade rice flour, wash and soak the raw rice for 2 hours. Spread on a clean paper or cloth and let it air dry for 10 minutes. Grind the rice in batches into a slightly coarse powder (fine to sight, but slightly coarse to touch for that authentic shop-style texture). Sieve and set aside. Rice flour is ready.

For syrup, powder the jaggery and add water just to cover it. Melt on medium flame and strain through a metal strainer to remove impurities. Return the syrup to medium heat and boil until it reaches soft ball consistency (uruttu padham). Test by dropping a bit in water; it should hold together into a loose, pliable ball without dissolving. Stir in cardamom powder and turn off heat.

Take the prepared rice flour in a wide bowl and add sesame seeds if using. Make a well in the center and pour the hot jaggery syrup little by little. Mix with a spatula into a soft, pliable, slightly gooey semi-solid dough. Do not add all syrup at once, as the dough will thicken as it cools.

Transfer the dough to an airtight container once cooled. Allow it to ferment at room temperature for 1 to 2 days (do not refrigerate). On the day of making, take the rested dough and divide into small lemon-sized balls.

Grease a thick plastic sheet, butter paper or banana leaf with oil or ghee. Place a dough ball and gently pat it with your fingers into a small round disc, about the thickness of a poori.

Heat oil in a kadai on medium heat. Drop a tiny bit of dough to check temperature; it should rise immediately. Gently slide in one adhirasam. It will puff up and turn golden brown quickly. Immediately flip and cook the other side for 1 to 2 seconds until bubbles subside.

Remove from oil, place between two flat ladles and press gently to drain excess oil. Drain on kitchen paper towels. Stack the adhirasams once warm to retain their soft texture and store in an airtight container.