Soak the beans overnight. Rinse and drain them.

Heat 1/3 cup of olive oil in a large pot over medium heat and cook the onions, carrots and celery together until softened, about 10 minutes. Add the beans and toss to coat in the oil. Pour in the water. Raise the heat and bring to a boil. Lower the heat and let the beans simmer, skimming the foam off the top, for about two hours, or until the soup is thick and creamy and the beans and vegetables very soft. About 10 minutes before removing from heat, add the salt and pepper. Stir in vinegar to taste. As soon as the fasolada comes off the stove, pour in the remaining olive oil. Serve hot.