Soak the white beans in the brine (salt water) overnight, OR bring beans to a boil for 2 minutes in salt water, and allow them to soak in the brine, covered, for two hours.
Drain the salt water/brine off the beans by straining through a colander.
Return beans to pot and add a hambone, the garlic, the onion, the carrot, parsley, a tablespoon of salt, a teaspoon of freshly ground black pepper, and about ¼ cup of olive oil.
Bring the beans and the vegetables and water to a boil, and then reduce the heat to low.
Simmer them for about 2 hours, tasting them at an hour and half, to check for doneness, between your teeth.
Before serving: Remove ham bone, onion halves, garlic head halves and chunks of carrot and celery, and parsley stems.
If there is any meat on the ham bone, you can cut that off and return it to the beans.
If you like, garnish each bowl with a small squeeze of lemon juice, and a drizzle of extra virgin olive oil.
