Begin by placing the chicken breasts in a large soup pot or Dutch oven. Pour in enough chicken broth to cover the chicken by about an inch. If necessary, add water to achieve this level.
While the chicken is cooling, add the sliced leeks, carrots, celery, diced potatoes, and dried thyme to the broth in the pot. Bring the broth back to a boil, then reduce the heat and simmer for about 10 minutes, or until the vegetables are tender.
Stir the shredded chicken and half and half into the pot with the vegetables. Season the soup with kosher salt and freshly ground black pepper to taste. Continue to cook and stir the soup until it is thoroughly heated. Serve the soup in bowls, garnished with chopped fresh parsley if desired. DEVOUR!