1. In a 4-quart soup pot or cast iron casserole (with a lid that fits), heat 1/4 cup of olive oil and cook the leeks, carrots and onions over medium-low heat until just softened, 8 to 10 minutes.
2. Add the dried beans and 12 cups of water. Bring to a simmer over high heat, then reduce the heat to low and cover the pot with the lid, stirring occasionally. After about 45 minutes, add 1 tablespoon of kosher salt. Continue to cook, covered, and again stirring occasionally, just until the beans are soft, 45 minutes to 1 hour or more (this may vary according to the beans you use).
3. With a slotted spoon, remove 1 cup of the beans and, separately, 2 tablespoons of bean liquor and set both aside. Add the kale to the soup, stirring in a few cups at a time as the greens wilt. Cover, and continue to cook for 8 to 10 minutes more until the greens are tender, then remove from the heat.
4. Meanwhile, bring a pot of salted water to a rolling boil and cook the pasta until al dente. Drain and reserve.
5. In a food processor, combine the reserved beans and bean liquor, sage, parsley, paprikas and lemon juice, the remaining 2 1/2 tablespoons olive oil and a pinch of salt. Blend until smooth, then check for seasoning, adding more salt if desired, or bean liquor to aid in blending.
6. Just before serving, stir the cooked pasta into the soup. Ladle the soup into bowls and top each with about 2 tablespoons of spiced bean purée. Grate Parmesan over the top of each bowl to taste and serve immediately.