Add chicken broth, celery, cabbage, onions and carrot to a large pot and bring to a boil. Reduce heat and simmer 20 minutes or until vegetables are tender.
Stir together cream and milk in a bowl.
In a medium saucepan, melt butter over medium heat. Add flour, salt and pepper. Stir to form a smooth paste. Gradually add cream and milk mixture, stirring constantly. Continue to cook and stir until it reaches desired thickness.
Gradually add cream mixture to vegetable mixture, stirring to combine. Add in ham and thyme. Heat through.