Serve this soup with warm dinner rolls or a half sandwich on the side. To vary the recipe, vary the vegetables in the soup—add broccoli or cauliflower florets, diced potato, or shredded chard. You can also add beans like cannellinis or black-eyed peas.
- In a large saucepan or small stockpot over medium heat, warm the oil. Add the onion and cook, stirring occasionally, until starting to become translucent, about 5 minutes. Add the carrots, celery, and garlic and cook, stirring occasionally, until the carrots and celery are crisp-tender, about 3 minutes. Add the ham, broth, cabbage, and bay leaves and bring to a boil over high heat. Reduce to a simmer, cover, and cook until the cabbage is tender, 15 to 20 minutes. Add salt and pepper to taste. Remove the bay leaves before serving.
- *To make ham broth, combine 2 smoked ham hocks, 1 carrot, 1 celery stalk, 1 onion (quartered), 2 bay leaves, 1 teaspoon whole peppercorns and 4 quarts water in a large stockpot. Bring to a boil over low heat, reduce to a very gentle simmer, cover and cook until the meat falls off the ham hocks, 3 to 4 hours. Strain the broth and add salt and pepper to taste. Makes about 3 quarts.