In a large dutch oven over medium heat, melt the butter. Add onion, celery and carrots and cook for 5 to 7 minutes, or until the onion is translucent and the vegetables are beginning to soften. Add garlic, rosemary and thyme and cook for 1 minute more, or until very fragrant. Season with salt and pepper.

Add the flour, stirring with a wooden spoon to evenly coat the vegetables. Add chicken stock, whisking to avoid lumps. Increase the heat to medium high and bring the liquid to a boil. Add chicken breasts, then reduce to a simmer. Cover and cook, stirring occasionally, for 20 minutes or until the chicken is cooked through.

Remove the chicken from the pot and set aside on a cutting board. Bring the soup back up to medium heat, and add egg noodles and milk. Cook, stirring occasionally, for about 8 minutes, or until noodles are tender.

Shred the chicken with two forks. Add chicken back to the pot, along with fresh parsley. Stir everything to combine and serve.