Combine the fava beans with enough water to cover by 2 inches in a large pot over medium-high heat. Add the garlic, lentils (if desired), and tomato. Bring to a boil, then reduce the heat as low as possible and simmer uncovered, for 12 hours, until the beans are very creamy and soft. Periodically add water to keep the beans covered.

You can also make these in a slow cooker: Boil for 10 minutes in a pot, then transfer to a slow cooker and cook on low for 12 hours. Remove the lid and cook on high for another 1 to 2 hours to reduce the liquid until it's barely creamy.

Stir in the salt, 3 tablespoons of the lime juice, the olive oil, and cumin and let the beans sit for at least 1 hour to absorb the seasonings. You can refrigerate them in an airtight container at this point for up to 1 week.

When you're ready to finish the beans, return them to the large pot over medium heat and use a potato masher to mash about half of them. (Alternatively, you can transfer half of them to the bowl of a food processor or blender and blend very briefly, then return them to the pot.)

While the beans are reheating, combine the parsley, onion, sumac, and the remaining 2 tablespoons lime juice in a bowl and toss to combine.

When the beans are hot, divide them among serving dishes or bowls and top with the parsley-onion mixture. Drizzle with a little olive oil and tahini and serve immediately.