01 -
In a large Dutch oven or heavy pot, combine the chicken broth, chopped celery, shredded cabbage, chopped onion, and chopped carrot. Bring the mixture to a boil over medium-high heat. Once boiling, reduce the heat to medium-low and simmer for about 20 minutes, or until all the vegetables are tender when pierced with a fork.
02 -
While the vegetables are simmering, stir together the half and half cream and milk in a medium bowl. Set aside.
03 -
In a separate medium saucepan, melt the butter over medium heat. Once melted, add the flour, salt, and pepper. Stir constantly with a wooden spoon or whisk until the mixture forms a smooth paste, about 1-2 minutes. This is your roux, which will thicken the soup.
04 -
Gradually pour the cream and milk mixture into the roux, stirring constantly to prevent lumps from forming. Continue to cook and stir over medium heat until the sauce reaches your desired thickness, about 5-7 minutes. The sauce should coat the back of a spoon.
05 -
Slowly pour the cream sauce into the pot with the vegetables, stirring constantly to incorporate. Add the cubed ham and dried thyme, stirring to distribute evenly throughout the soup. Heat through for another 5 minutes, stirring occasionally.
06 -
Ladle the hot soup into bowls and garnish with chopped fresh parsley if desired. Serve immediately with crusty bread for a complete meal.