Slice each leek in half lengthwise, then slice each half into 1/4-inch-thick half-moons (about 2 cups). Place in a large bowl of cold water and swish to remove any grit. Drain and pat dry.
Remove the stems from the kale. Stack the leaves on top of one another and slice them crosswise into 1/2-inch-wide strips; you'll need 3 cups.
Heat the oil in a saucepan over medium heat. Add the leeks and cook for 3 minutes. Add the tomatoes and cook, breaking them up with a spoon, for 5 minutes. Add the water and bring to a boil. Stir in the kale, sweet potatoes, lentils, thyme, salt, pepper, and basil (if using). Simmer until the lentils are tender, about 30 minutes. Spoon into individual bowls. Sprinkle with the Parmesan (if using).
Tip: Basic brown lentils retain their shape better during cooking than pricier red and yellow lentils, so they're terrific for soups. You can substitute green lentils, which taste slightly peppery.
To Freeze: Omit the Parmesan. Let the soup cool, then ladle into large resealable bags, filling each one halfway. Store for up to 3 months.
To Reheat: Thaw overnight in the refrigerator or thaw partially in the microwave. Warm in a covered saucepan over medium heat for 20 minutes. Ladle into individual bowls and sprinkle with the Parmesan (if using).