Remove seeds, if any from the tamarind and soak it in half a cup of hot water to allow the tamarind to soften a bit.
In a small pan, heat 1 teaspoon of oil and fry the coriander seeds, channa dal, toor dal, urad dal and red chilies until light brown. At the end add the pepper and cumin and fry for about 15 seconds. Do not fry longer after you add the pepper and the cumin as it becomes bitter. Let the mixture cool down a bit.
Grind the cool mixture to a coarse powder and then add the soaked tamarind along with the water into the mixer and grind it into a smooth paste. Add about 2 cups of water and mix it well.
In a pan, heat 3 tablespoon of gingelly oil (or any cooking oil). Add the mustard seeds and let it splutter. Now add the asafetida and curry leaves and let it fry for about 10 seconds.
Slowly add the ground mixture and add salt needed. Let it come to a gentle boil and then add the jaggery.
Simmer the kuzhambu for about 20 to 30 minutes or until it thickens and the oil starts leaving the sides of the pan. Make sure you stir it every now and then so that it does not stick to the bottom of the pan.
Serve the kuzhambu with hot rice and ghee. I made paruppu thuvayal and tomato pachadi along with Milagu kuzhambu to make it a meal.