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 and onion becomes translucent.
02 - Stir in minced garlic and cook for 1 minute until fragrant, being careful not to burn the garlic.
03 - Sprinkle flour over the vegetables and stir constantly for 2 minutes to cook out the raw flour taste. The mixture should form a thick paste coating the vegetables.
04 - Gradually whisk in chicken broth, adding about 1 cup at a time and ensuring no lumps form before adding more. Bring mixture to a gentle simmer.
05 - Add shredded chicken breast, dried thyme, salt, and black pepper. Simmer covered for 15 minutes until vegetables are completely tender.
06 - Reduce heat to low. Pour in whole milk and heavy cream, stirring gently to combine. Heat for 5 minutes until warmed through, taking care not to let the soup reach a boil.
07 - Stir in fresh chopped parsley. Taste and adjust salt and pepper if needed.
08 - Ladle hot soup into bowls and garnish with additional fresh parsley. Serve immediately while hot.