In a large pot, melt the unsalted butter over medium heat.
Add the diced onion, minced garlic, diced carrots, and diced celery to the pot. Cook, stirring occasionally, until the vegetables are softened, about 5-7 minutes.
Stir in the dried thyme, dried rosemary, salt, and black pepper. Cook for 1 minute to release the flavors.
Pour in the chicken broth and bring the mixture to a boil.
Reduce heat to low and simmer for 15 minutes, allowing the flavors to meld and the vegetables to become tender.
Add the shredded cooked chicken breast to the pot and stir to combine.
In a small bowl, whisk together the all-purpose flour and cold water until smooth to create a slurry.
Slowly pour the slurry into the soup while stirring continuously to avoid lumps.
Add the heavy cream to the soup and stir well.
Continue cooking the soup on low heat for another 5-7 minutes until it thickens and becomes creamy.
Taste and adjust seasoning with additional salt and black pepper if needed.
Remove from heat and stir in the chopped fresh parsley.
Serve hot and enjoy your creamy chicken soup.