In a large heavy-bottomed pot, heat the coconut oil over medium-high heat. When the oil is hot and shimmering, add the cumin seeds and mustard seeds (if using) and cook for 1 minute, until the seeds begin to pop.
Add the onions, carrots, and ginger to the pot and cook until the onions are tender, about 5 minutes.
Add the turmeric, salt, pepper, rice, and red lentils. Stir to coat the rice with the spices.
Add the water and bring the mixture to a boil. Reduce the heat to simmer and cook, covered, for 15 minutes.
Check the pot to see if the rice and lentils are tender. If they are not but there is no more liquid, add an extra 1/2 cup water and cook for an additional 5 minutes.
If the rice is tender but the mixture contains a lot of liquid, simmer uncovered for an additional 3 to 5 minutes.
Serve the kitchiri with the chopped cilantro.
