1. In a skillet, saute ham, onion and garlic in butter until onion is tender.
2. Peel potatoes and add to a saucepan and cover with water. Bring to boil and then turn down to medium and continue to cook for 15 minutes or until potatoes are soft. Drain and rinse with cold water. Let rest for 5 minutes before chopping.
3. Take 1 can of drained beans and puree in blender with a little bit of water until thick and smooth.
4. To a large stockpot, combine sauteed items, chopped potatoes, pureed beans and the next 8 ingredients. Stir well to combine. Bring to a boil and then simmer for 40 minutes or until vegetables are tender.
5. To thicken the soup, stir together cornstarch and water until smooth. Slow stir into soup pot. Continue to cook for 5 more minutes to allow soup to thicken.