In a flat-bottomed frying pan or skillet, dry roast the rice without letting the colour change. Wash and soak it for about half an hour in cold water then drain and spread on a cotton cloth to absorb the excess moisture. Grind the rice to a fine powder.
In the same flat-bottomed frying pan or skillet, dry roast the split black gram to light brown colour, cool and grind also into a smooth powder then sieve both the 'flours' together through a fine sieve.
Dissolve the asafoetida and salt in 2 fl oz (60ml - ¼ cup) water and add the cumin seeds. Mix with the sieved flour to make a firm dough then rub in the butter and knead gently to mix well.
To make the murukkus, grease your fingers and take a little of the dough about the size of a golf ball. Roll this between your palms to form a tubular shape then gently pinch one end between finger and thumb and begin to roll out the dough in a continuous circle, twisting the ball of dough as you work. Keep storing them on a plate and make two batches at a time, cover with a wet cloth to prevent them from drying.
Heat 2"-3" (5-8cm) oil in a deep pan and, once the oil is hot, turn the heat down to medium. Take the plate of circles to the pan and gently slide them one by one into the oil and fry until they float to the top and the 'shhhh…' sound ceases. Flip them over to fry until both sides are a golden colour and the Murukku are crisp.
Carefully remove from the oil and allow them to drain on absorbent kitchen paper. Once they are cooled, store in airtight container. The flavour is at its best when eaten the following day.