Place the (unsoaked!) dried beans in a smaller pot with 4 cups of cold water and just ½ teaspoon of salt. Turn on the heat to medium and bring to a gentle boil, then turn down the heat to the lowest setting and cover with a lid. Keep simmering until cooked (between 3- and 3 ½ hours).

Meanwhile, chop the carrot, onion, and celery. Mince the garlic. Peel and dice the potatoes, clean and cut the remaining vegetables into ½-inch slices or cubes. Set aside.

When the beans are cooked, drain them, reserving the cooking water. In a blender or food processor, puree about ¾ of the beans and return the bean purée to the cooking water. Set aside. Also set aside the remaining whole beans.

In a large pot, prepare the soffritto: heat ⅓ cup extra-virgin olive oil, and sauté the carrot, celery, garlic and onion over medium-high heat, until golden in color, about 7-8 minutes. Stir often to avoid burning.

Add the thyme leaves, the remaining ½ tsp. of salt, the remaining fresh vegetables, the tomato paste, the bean purée with its water, along with an additional 4 cups of water. Cook over low heat, covered, for about 1 hour.

Finally, add the previously cooked whole beans and the stale bread, cut into ½-inch slices, crust on. Stir, cook for another 5 minutes and turn off the heat.

Let soup sit for at least a few hours, ideally overnight. Then, reheat the soup, boiling for a few minutes at low heat.

Serve sprinkled with freshly ground black pepper and drizzled with a little high-quality extra-virgin olive oil.