In a large pot, melt the butter over medium heat. Add onion, carrots, and celery; sauté until softened, about 5 minutes.
Stir in garlic and cook for 1 minute. Sprinkle flour over the vegetables and stir for 1-2 minutes until lightly golden.
Gradually whisk in chicken broth and milk, stirring until smooth and slightly thickened.
Bring to a boil, then reduce heat and simmer for 5 minutes. Add rotisserie chicken and noodles; cook until noodles are tender, about 8-10 minutes.
Season with salt and pepper to taste. Garnish with fresh parsley before serving.