Bring a pot of salted water to a boil and cook the pasta for 8 minutes. Drain and set aside.
Melt butter in a large pot over medium-low heat. Add onion and celery; cook for 3 minutes. Stir in garlic for 30 seconds.
Sprinkle flour over the vegetables and cook for 1 minute, stirring constantly.
Add chicken broth, carrots, bay leaves, turmeric, paprika, and salt. Bring to a boil, then simmer uncovered for 15–20 minutes until carrots are tender.
Stir in milk and gently simmer. Lower heat and add Parmesan cheese, stirring until melted.
Add chicken, cooked pasta, rosemary, and parsley. Stir well. Adjust salt and broth as needed.
Let the Creamy Chicken Parmesan Pasta Soup rest for 15 minutes. Remove bay leaves and serve.