Heat the coconut oil in a heavy-bottomed pot over medium heat. Add the mustard seeds and cumin seeds and toast them until the mustard seeds start to pop, about 1 to 2 minutes. Add the onions, carrots, ginger, and garlic. Cook for about 5 minutes, stirring frequently to keep the vegetables and spices from burning.

Once the onions have softened, add the salt, turmeric, cloves, and black pepper and stir until the spices coat the vegetables. Add the rice, moong dal, vegetable broth, and water. Bring everything to a boil, then reduce the heat to low. Cover the pot and simmer the kitchari for about 20 minutes. After 15 minutes of cooking, check to see if there are still enough liquids in the pot. If you notice that the liquids are completely absorbed by the rice and beans, add 1/2 to 1 cup of water and stir to incorporate.

Remove the lid and check to see if the rice is tender. If the kitchari is looking too runny, let it simmer, uncovered, for a few more minutes. If the kitchari is too thick, turn off the heat and add 1/2 to 1 cup of water and stir. Taste and see if you need to add a small pinch of salt.

Serve the kitchari in bowls, along with chili oil, cilantro, and lemon wedges, if you like.