In a large bowl, combine the beans with 8 cups water and 1 tablespoon salt. Stir, then let soak at room temperature for at least 12 hours or up to 24 hours.

Drain the beans and add them to a large pot along with the tomatoes, leek, garlic head, bay, thyme and 9 cups water. Bring to a boil over medium-high, then reduce to medium and cook, uncovered, stirring occasionally and adjusting heat to maintain a simmer, until the beans are tender, 45 to 55 minutes.

Meanwhile, in a food processor, combine the basil, Parmesan, 2 tablespoons of oil, the garlic cloves, pine nuts and ½ teaspoon salt. Process until the mixture has a spreadable consistency, 30 to 60 seconds, scraping the bowl as needed. Transfer the pistou to a small bowl and set aside.

In a small saucepan over medium, heat the remaining 1 tablespoon olive oil until shimmering. Add the pasta and cook, stirring often, until toasted, about 3 minutes. Remove from the heat and set aside.

To the beans, add the carrot, 4 teaspoons salt and ½ teaspoon pepper. Continue to cook, stirring occasionally, until the carrots are barely tender, 5 to 7 minutes.

Stir in the toasted pasta and zucchini, then continue to cook until the pasta and zucchini are tender, 6 to 10 minutes.

Remove and discard the bay. Using tongs, remove the garlic head from the pot and squeeze the base of the head to release the cloves into the pot. Using the tongs, gently squeeze any tomatoes that are still whole so they burst.

Taste the soup and season with salt and pepper. Ladle the soup into bowls. Swirl 1 tablespoon of pistou into each; serve with the remaining pistou on the side.