- Make the basil pistou: Fill a large saucepan with water and bring it to a boil. Fill a large bowl with ice and cold water and set it nearby. Add 1 teaspoon salt to boiling water. Blanch basil in boiling water for about 20 seconds, until it develops a bright green color, and then immediately plunge it into the ice bath. After a minute, strain basil from water, wrap it in a kitchen towel, and squeeze gently to remove excess water.
- Place basil, cheese, and pistachios in a food processor and turn it on. Slowly drizzle in olive oil. Season to taste with salt and pepper. Refrigerate, covered, until ready to use. The pistou will keep in the fridge for about 1 week.
- Make the soup: Place beans in a large bowl and add cold water to cover by 3 inches. Cover bowl and soak beans in the refrigerator overnight.
- The next day, in a medium skillet over medium heat, warm 2 tablespoons of olive oil. When oil is shimmering, add onions and sauté until softened, about 5 minutes, then remove from heat.
- Drain beans and add to a 4-quart (or larger) slow cooker. Add stock, onions, carrot, and celery. Cover with lid, turn to low setting, and cook for 6 to 8 hours, until beans are tender but not busted. Stir in ground fennel, tomatoes, zucchini, pepper, and 1 tablespoon salt. Cover and cook for 1 hour more.
- Season to taste with additional salt. Ladle soup into individual bowls and garnish each with basil pistou and a drizzle of olive oil.