Start by melting the butter in a large soup pot over medium heat. Add the chopped onions, celery, and minced garlic.
Sauté for a few minutes until fragrant. Stir in the sliced mushrooms, fresh rosemary, and dried thyme, cooking until the mushrooms are tender.
Pour in the dry sherry to deglaze the pot, scraping up any browned bits. Add the whole chicken breasts, chicken broth, 1 teaspoon salt, and 1/4 teaspoon black pepper. Bring it to a boil, then reduce heat and simmer for about 15 minutes until the chicken is cooked through.
Carefully remove the cooked chicken breasts, then chop them into bite-sized pieces.
In a small bowl, whisk the cornstarch (or arrowroot) into the heavy cream until smooth. Pour this mixture into the simmering soup, stirring continuously until it thickens nicely. Return the chopped chicken to the pot, stir in the fresh parsley, and adjust seasoning with salt and pepper to your liking.