Warm the oil in a medium saucepan over medium heat. Add the onion and carrots and sauté, stirring frequently, until they are tender and the onion is translucent, about 8 minutes. Add the tomatoes, kale, rosemary, and water. Bring to a boil.
Reduce the heat to low, and simmer for 30 minutes. Add the beans, and simmer 15 minutes more. Season with salt and pepper to taste.
Whisk in the cornmeal in a thin, steady stream. Simmer, whisking often, until the soup has thickened and the polenta is tender, about 5 minutes. Spoon the soup into serving bowls, and if desired, serve topped with cubed cheese and additional olive oil.