Grind the tomatoes in a mixie. Do not grind the tomatoes to a fine puree. Just pulse for a few times. The tomatoes should remain in bits. Set aside.
In a mortar and pestle, grind the pepper and cumin seeds to a coarse powder. Once the pepper and cumin is coarse, add in the garlic cloves. No need to peel the garlic. Crush the garlic ans set aside.
Heat sesame oil in a pan and add in the mustard seeds. Let the mustard seeds splutter. Add in the ground pepper-cumin-garlic mixture. Saute for a few seconds.
Add in the curry leaves and the dried red chillies.
Add in the roughly pureed tomatoes. Also add in the turmeric powder, asafoetida and salt. Saute for a minute.
Soak a small gooseberry size tamarind in a cup of water for 15 minutes. Squeeze the tamarind well to extract the pulp. Discard the seeds and the pith. Add in the tamarind pulp to the pan.
Add in the rice water (kalani) to the pan.
Let the rasam come to a boil. Do not allow the rasam to boil for a long time. When the rasam becomes frothy and the sides starts to bubble up, remove the rasam from heat. Add in the coriander leaves and green chillies. The green chillies is optional.