01 - Melt butter in a large pot over medium heat. Add onion, celery, and carrots. Sauté for 4-5 minutes until vegetables begin to soften and release their aroma.
02 - Stir in minced garlic and cook for 1 minute until fragrant, being careful not to brown the garlic.
03 - Sprinkle flour into the pot and stir constantly for 2 minutes to cook out the raw flour taste. The mixture should form a smooth paste and bubble gently.
04 - Gradually whisk in chicken broth, ensuring no lumps form as you pour. Bring the mixture to a gentle simmer while continuing to whisk.
05 - Add cooked chicken, thyme, salt, and pepper. Let the soup simmer uncovered for 15 minutes until vegetables are completely tender.
06 - Reduce heat to low. Pour in milk and heavy cream, stirring gently to combine. Heat for 5 minutes until warmed through, but do not allow to boil as this may cause separation.
07 - Stir in fresh parsley and taste for seasoning, adding more salt or pepper if desired. Serve immediately in bowls, garnished with additional fresh parsley.