Rinse the rice and toor dal thoroughly and add them to a large heavy-bottomed pot with the chopped vegetables, tomato, onion, turmeric, salt, and about 4 cups of water. Bring to a boil, then reduce the heat, cover, and cook until the rice, dal, and vegetables are very soft and creamy. While they cook, heat the oil or ghee in a small pan and add the mustard seeds, cumin seeds, dried red chili, curry leaves, and asafoetida. Once the spices begin to crackle, add the sambar powder and sauté briefly until fragrant, being careful not to burn it. Stir this tempering into the cooked rice and dal mixture, then add the tamarind paste and enough remaining water to create a thick, porridge-like consistency. Simmer everything together for another 5–7 minutes, stirring occasionally so the flavors blend beautifully. Taste and adjust the salt, tamarind, or sambar powder as needed, then garnish with fresh coriander and serve hot.