In a large Dutch oven, combine the broth, celery, cabbage, onion and carrot; bring to a boil. Reduce heat; cover and simmer for 15-20 minutes or until vegetables are tender.
Meanwhile, melt butter in a small saucepan. Stir in the flour, salt and pepper until blended. Combine cream and milk; gradually add to flour mixture. Bring to a boil; cook and stir for 2 minutes or until thickened. Gradually stir into vegetable mixture. Add ham and thyme and heat through. Garnish with parsley.