Heat oil in a large Dutch oven over medium heat. Add leek, carrot, and celery; cook 8 minutes or until tender, stirring occasionally. Stir in broth and next 8 ingredients (broth through tomatoes); bring to a boil.
Reduce heat; simmer 20 minutes or until vegetables are tender. Stir in cabbage; cover and cook 1 minute or until cabbage wilts. Stir in parsley.