FOR THE SOUP:
1 pound dried cannellini beans
¼ cup smoked turkey, cut in small chunks
1 yellow onion, quartered lengthwise
1 celery stalk, quartered crosswise
1 carrot, quartered crosswise
2 cloves garlic, peeled and lightly crushed
1 bay leaf
1 quart chicken stock
Finely ground sea salt, preferably gray salt
2 tablespoons extra-virgin olive oil
FOR THE BASIL TOPPING:
1/4 cup extra-virgin olive oil
1 tablespoon minced garlic
1/4 to 1/2 teaspoon red pepper flakes
1/4 cup lightly packed fresh basil leaves
Sea salt and freshly ground black pepper
Cook the beans: Rinse the beans, place in a saucepan, and add cold water to cover by 2 inches. Bring to a boil, cover, and remove from the heat. Let stand for about 20 minutes, then drain.
Return the beans to the saucepan along with the smoked turkey, onion, celery, carrot, garlic, and bay leaf. Pour in the chicken stock and then add water as needed to cover the beans by 2 inches. Slowly bring to a simmer over medium-low heat. (If you heat them too fast, the skins may break.) Adjust the heat to maintain a bare simmer and cook, uncovered, until the beans are almost tender, 20 minutes or longer. Add salt, to taste, and continue cooking until the beans are tender but not mushy, about 20 minutes longer. Remove from the heat and let the beans cool in the liquid.
Strain the cooled beans and other solids through a sieve, reserving the liquid. In a food processor or with a hand blender, puree the beans and solids in batches with 3 1/2 cups of the cooking liquid and 2 tablespoons olive oil.. Season, to taste, with salt and pepper, then bring to a simmer over medium heat, stirring occasionally.
Meanwhile, in a small skillet over high heat, warm the 1/4 cup olive oil. Turn on the fan above your stove. Add the garlic to the skillet and cook, stirring occasionally, until it begins to turn brown. Add the red pepper flakes and cook for a few seconds, then add the basil. Cook until basil wilts.
To serve, ladle the hot soup into warmed bowls. Top the soup with the basil mixture.