Rinse split peas in several changes of water until the water runs clear. Drain. Add 3 cups of water and turmeric and bring to a boil. Skim foam and simmer the peas, uncovered, until they are cooked but al dente, approximately 30 minutes.
Add 2 more cups water and simmer until tender, approximately 15 more minutes.
In the meantime, heat 2 tablespoons ghee in a large pan on high heat. Add onion, raisins, and bay leaves, and cook for about 10 minutes, stirring occasionally, until the onions look almost fried. Remove from pan.
In pan, heat the remaining 1 tablespoon ghee over medium heat. Add cumin seeds and cook just until they sizzle, which will be almost immediately. Add ginger and garlic and cook for a minute, stirring.
Add tomato, chiles, salt, garam masala, and 1 cup water. Scrape all the good bits off the bottom of the pan.
When the peas are tender, add the tomato-cumin mixture to the peas and simmer, uncovered, for another 15 minutes or so, until the tastes meld.