Rinse the rice and moong dal together several times until the water runs mostly clear, then drain. Heat the ghee in a heavy-bottomed pot or pressure cooker over medium heat and add the cumin seeds and asafoetida. Once fragrant, add the onion, ginger, garlic, and green chili and sauté until the onion becomes soft. Add the tomato, carrot, potato, turmeric, black pepper, and salt, stirring for 2–3 minutes until the vegetables begin to soften. Add the rinsed rice and dal along with the water and stir everything together. Bring to a gentle boil, then cover and simmer for about 25–30 minutes, stirring occasionally, until the rice and dal become very soft and creamy. Add a little extra hot water if needed to reach your preferred consistency. Garnish with fresh coriander and serve warm with a spoonful of ghee, yogurt, or pickle.