Step 1

Place 8 ounces dried chickpeas in a medium saucepan and add enough cool water to cover by at least 2 inches. Repeat with 8 ounces dried cannellini beans in a second medium saucepan. Let soak at cool room temperature or in the refrigerator for at least 8 hours or up to overnight.

Step 2

Place 1 pound Parmesan cheese rinds, 5 fresh parsley sprigs, 5 fresh thyme sprigs, and 2 teaspoons whole black peppercorns in a large pot or Dutch oven. Remove 5 outer leaves from the leeks for the soup base, rinse clean, and add to the pot. Add 12 cups (3 quarts) water and bring to a boil over high heat, stirring occasionally.

Step 3

Reduce the heat so that the liquid is barely simmering and cook, stirring every 10 to 15 minutes with a heatproof spatula to keep the cheese from sticking to the bottom, until the broth is cloudy, intensely flavorful with cheese, and reduced by about half, 2 to 3 hours. (This is a good time to cook the beans.)

Step 4

Remove the pot from the heat and let cool slightly, about 15 minutes. Line a fine-mesh strainer with cheesecloth and place over a large bowl. Pour the broth through the strainer; you should have 6 to 8 cups broth. If you have less, make the difference up with water to get at least 6 cups. Discard the contents of the strainer.

Step 5

Drain the beans and return to their respective saucepans. Add the following to each saucepan: 3 peeled garlic cloves, 2 fresh oregano sprigs, 2 fresh thyme sprigs, 1 fresh rosemary sprig, and 1 bay leaf. Add enough water to each pan to cover the beans by at least 2 inches.

Step 6

Bring each saucepan to a boil over high heat. Reduce the heat to maintain a simmer and cook until the beans are tender, 1 1/4 to 2 hours. (This is a good time to prep the vegetables for the soup base.)

Step 7

Strain each pot of beans through a fine-mesh strainer into a heatproof bowl and reserve both the beans and cooking liquid. Do your best to pick out any large chunks of garlic and herbs, but it’s OK if a little bit of cooked herbs remain in the beans.

Step 8

Place 2 cups of the cannellini beans, 1 cup of their cooking liquid, and 1 teaspoon kosher salt and a few grinds of black pepper in a food processor fitted with the blade attachment. Process until a smooth paste forms, about 1 minute. Transfer to a large bowl. Repeat blending the same amount of chickpeas, cooking liquid, and salt; transfer to the same bowl of cannellini bean paste. You should have both bean paste and whole cooked beans now.

Step 9

Dice 1 medium white onion. Place the onion, 2 tablespoons unsalted butter, and 1 teaspoon kosher salt in a Dutch oven or large pot over medium heat. Cook, stirring occasionally and reducing the heat as needed, until the onions are lightly caramelized, 20 to 30 minutes.

Step 10

Meanwhile, peel and dice 3 medium carrots and dice 3 celery stalks (1 1/4 cups each). Trim 2 medium leeks and remove any tough dark outer leaves. Cut in half lengthwise and rinse away any dirt. Cut into the same size as the carrots and celery (about 2 1/2 cups).

Step 11

Add the leeks and cook over medium heat until softened, about 3 minutes. If the leeks absorb all the butter, add 1 tablespoon olive oil or bean cooking liquid to the pot. Add the carrots and celery and cook until all the vegetables are soft and aromatic, 4 to 5 minutes. Meanwhile, bring a large saucepan of salted water to a boil.

Step 12

Add 6 cups of the broth to the vegetables and bring to a simmer over medium-high heat. Add the bean pastes and stir to combine. Add the whole cooked beans, stir to combine, and bring to a simmer. Taste and season with kosher salt and black pepper as needed.

Step 13

Add 12 ounces dried ditalini pasta (scant 2 1/2 cups) to the boiling water and cook according to package directions. Drain and rinse under cold water. To serve, add some cooked ditalini to each bowl, then ladle a generous helping of pasta fagioli on top. Garnish with celery leaves and serve with crusty bread or garlic bread.