Cut all vegetables into large chunks and place in food processer. It is not necessary to peel carrots and potatoes as long as they are thoroughly washed. Carefully pulse just enough to break vegetables into bite-sized chunks. Do not over pulse. Add broth, full ham steak including the bone and bay leaves to a large stockpot, and bring to a boil. Reduce heat to low and add vegetables and remaining ingredients except 1 can of beans. Simmer with lid on pot until vegetables are tender. Remove meat and bay leaves from pot and let meat cool on a cutting board. Discard bay leaves and ham bone. Pour 1 can of beans into food processer and pulse to a paste, add them to the pot and stir well. Once cool enough to handle, chop ham into bite-sized chunks and replace into pot. Reheat soup and serve.
I usually use chicken broth and add a tablespoon of ham bouillon, omitting the salt.