In a medium bowl, cover the beans with water by at least 1 inch and leave them in the refrigerator for 6 hours or overnight. Drain.

In a large stockpot over low to medium heat, saute the onions with the olive oil until the onions are translucent, 10 to 15 minutes.

Add the garlic and cook over low heat for 3 more minutes.

Add the drained white beans, rosemary, chicken stock, and bay leaf.

Cover, boil, and simmer for 30 to 40 minutes until the beans are very soft.

Remove the rosemary branch and the bay leaf.

Pass the soup through the coarsest blade of a food mill, or place it in the bowl of a food processor fitted with a steel blade and pulse until coarsely pureed. If you don't own a food processor a potato masher will work.

Return the soup to the pot to reheat and add ham and salt and pepper, to taste. Serve hot.