Pressure cook the pigeon peas/toor dal with 1/2 cup water and a pinch of turmeric powder. Add 1 cup water to dal and mash well.
Soak the tamarind in 1 cup water and extract the pulp.
In a vessel, add tamarind water, tomato, rasam powder, red chilly powder, jaggery and salt. Mix well and bring to boil. Boil for 3-4 minutes.
Add the cooked dal to the rasam and simmer till the rasam becomes frothy. Remove from heat.
In a tadka pan, heat ghee. Add mustard seeds and when it splutters add jeera, red chillies, asafoetida, curry leaves and pour into the rasam. Garnish with fresh coriander leaves.