Add the broth, diced onion, carrots, celery, garlic, chopped cabbage, potatoes, ham, parsley, rosemary, and black pepper to the slow cooker. Stir to combine so the vegetables are evenly distributed in the broth.
6 cups (1.4 L) low-sodium chicken broth, 1 large yellow onion, 2 large carrots, 3 celery ribs, 2 cloves garlic, 3 cups (180 g) chopped green cabbage, 2 cups (300 g) peeled and diced russet potatoes, 1½ cups (225 g) chopped ham, 1 tsp (2 g) dried parsley, ½ tsp (0.5 g) dried rosemary leaves, ½ tsp (0.5 g) coarse ground black pepper