Step 1

If you haven’t soaked the beans, do a power soak: Place beans in a large pot, cover with water by 1", and bring to a boil over high heat. As soon as the water comes to a boil, remove pot from heat, stir in a palmful of salt, cover pot, and let beans sit 1 hour.

Step 2

Pulse carrots, leek, and garlic in a food processor until finely chopped. Heat ⅓ cup oil in a large pot or Dutch oven over medium. Add chopped vegetables, season generously with salt and pepper, and cook, stirring often, until vegetables start to sweat out some of their liquid, about 4 minutes. The goal at this stage is to slow cook the soffritto until the vegetables are very soft but have not taken on any color. Reduce heat to medium-low, cover pot, and cook, stirring every 5 minutes or so and reducing heat if mixture starts to brown, until vegetables are softened and juicy, about 15 minutes. Add ham hock and cook, uncovered, stirring and scraping bottom of pot every 5 minutes, until soffritto is starting to brown in places and has lost at least half of its volume, about 10 minutes more.

Step 3

Add beans and their soaking liquid, tomatoes, and kale; season with salt and pepper. Bring to a boil, then add Parmesan rinds (if using) and bay leaves. Reduce heat to medium-low and bring to a gentle simmer. Cook soup with lid askew, adding water (or stock, if you have it) as needed to keep beans submerged by 1", until beans are very tender, 1–3 hours, depending on size and age of beans. Fish out and discard Parmesan rinds. Remove ham hock and use a fork to pull meat off the bone. Return meat to soup; discard bone and any large pieces of fat.

Step 4

Cook pasta in a large pot of boiling well-salted water, stirring occasionally, until very al dente, about 3 minutes less than package directions. Drain pasta and add to soup, then taste and season with more salt and pepper if needed. (Do not try to skip a step by cooking the pasta in the soup. The noodles will absorb all the available liquid and the liquid will be thick and gummy.)

Step 5

Divide soup among bowls. Top with Parmesan, drizzle with oil, and sprinkle with red pepper flakes. Serve with bread for dunking.