In a medium enameled cast-iron casserole, cover the yellow split peas, toor dal and red lentils with 1 1/2 inches of water. Bring to a boil and simmer over low heat, stirring occasionally, until the red lentils and toor dal break down and the split yellow peas are tender, about 1 hour and 15 minutes.
In a large skillet, heat the oil until shimmering. Add the cumin seeds and cook over moderate heat until they darken, 1 minute. Add the onion and garlic and cook, stirring, until golden brown, 6 minutes. Add the coriander, turmeric and cayenne and cook, stirring a few times, until fragrant, 2 minutes. Add the tomato and cook until softened, 3 minutes. Scrape the mixture into the dal and simmer over low heat, stirring occasionally, until the flavors are blended, 3 minutes. Season with salt. Stir in the butter and cilantro and serve.