Chop vegetables and set aside. Melt butter in a large saucepan. Add carrots, garlic, and celery and cook stirring frequently for about 5 minutes or until vegetables are soft.
Whisk in flour, salt, pepper, and thyme. Cook for about 1 minute.
Add chicken broth and potatoes, stir well and bring to a boil. Boil for a few minutes, reduce heat to low/medium and simmer with cracked cover for 20-25 minutes or until potatoes are soft.
Add milk, half and half, chicken, and noodles. Stir well and cook on medium heat for 10 minutes.