Soak the rinsed rice and toor dal together in water for at least 15-20 minutes.
In a pressure cooker or instant pot, heat oil and ghee. Then add mustard seeds, cumin seeds, curry leaves, hing, and black peppercorns. Let them sizzle.
Next, add chopped shallots (or red onions), garlic, and green chili. Sauté until the onions turn soft and translucent.
Next, add the chopped tomatoes along with rasam powder, turmeric, red chili powder, and coriander powder. Sauté for a few minutes until the tomatoes soften and the spices are fragrant.
Then, add the tamarind water (or tamarind paste), soaked dal, and rice. Pour in 3 cups of water and mix well.
Pressure Cook for 4 whistles on a medium-high flame, and turn off the flame. Allow the pressure to release naturally.
Add about 1 cup of boiling water, or as needed, to bring the rasam rice to a flowy, pourable consistency. Lastly, garnish with coriander leaves. One-pot rasam sadham is ready to serve.