In a large Dutch oven over medium heat, melt the butter. Add the onion, celery, and carrots and cook for 5–7 minutes, or until the onion is translucent and the vegetables begin to soften. Add the 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 the chicken stock, whisking to avoid lumps. Increase the heat to medium-high and bring the liquid to a boil. Add the 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, then add the egg noodles and milk. Cook, stirring occasionally, for about 8 minutes, or until the noodles are tender.

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