01 - Melt butter in a large pot over medium heat. Add chopped onion, diced celery, and carrots. Sauté for 4-5 minutes until vegetables begin to soften.
02 - Stir in minced garlic and cook for 1 minute until fragrant, being careful not to burn.
03 - Sprinkle flour over the vegetables and cook for 2 minutes, stirring constantly to form a smooth roux and eliminate raw flour taste.
04 - Gradually whisk in chicken broth, ensuring no lumps form. Bring mixture to a gentle simmer while stirring occasionally.
05 - Add cooked chicken, dried thyme, salt, and black pepper. Simmer uncovered for 15 minutes until vegetables are completely tender.
06 - Reduce heat to low. Stir in whole milk and heavy cream. Heat gently for 5 minutes, stirring frequently to prevent scorching. Do not allow soup to boil.
07 - Stir in fresh chopped parsley. Taste and adjust seasoning if necessary. Serve hot in bowls, garnished with additional fresh parsley.