Dry roast the rice in a warm frying pan without letting the color change. Wash and soak for about ½ hour, drain and spread on a cotton cloth to absorb the excess moisture. Grind to a fine powder. Broil the urad dal to light brown color, cool and grind into a smooth powder. Sieve both the flours together through a fine sieve.
Dissolve asafoetida and salt in ¼ cup water and add the cumin seeds. Add it to sieved flour to make a firm dough. Rub in the butter and knead with light hands to fully incorporate the butter. To make the murukkus, grease your fingers and take a little dough. Roll them between your palm to a tubular form. Shape this roll into circles, twisting them along.
Make two circles next to each other. Press the ends into the circle to secure. Make two batches at a time, cover with a wet cloth to prevent them from drying. Heat oil and fry them in batches. Take them on a plate and gently slide them into the oil and fry on both sides till it becomes light golden brown and crisp. Drain and let it cool before serving them. Store in a dry air-tight container.