In a 1 1/2- to 2-quart pan, combine onion, carrot, garlic, cooked ham, and broth. Bring to a boil over high heat. Cover and simmer over medium heat until the carrot is soft to bite, about 10 minutes.
Stir in beans and simmer, covered, over low heat until beans are hot, about 5 minutes. Sprinkle with parsley and serve.