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 and slice 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 3 minutes. Add the tomatoes and cook, breaking them up with a spoon, for 5 minutes.
Add water and bring to a boil. Stir in the kale, sweet potatoes, lentils, thyme, salt, pepper, and basil (if using). Simmer until lentils are tender, about 30 minutes.
Top with Parmesan, if using, before serving.