Heat olive oil in a soup pot over medium-high heat. Cook and stir onion in hot oil until tender, about 5 minutes.
Season onion with Italian seasoning. Continue to cook and stir for 1 more minute.
Stir chicken broth, white beans, tomatoes, cabbage, ham, and celery into the pot. Bring to a boil, then reduce heat to low; simmer until celery and cabbage are tender, 15 to 20 minutes.