**Sauté the Vegetables:** In a large pot, melt butter over medium heat. Add the onion, carrots, and celery, and sauté for 5-7 minutes until softened. Stir in the garlic and cook for 1 more minute.
**Make the Roux:** Sprinkle the flour over the vegetables and stir well to coat. Cook for 1-2 minutes, stirring constantly, until the flour is lightly golden.
**Add the Broth:** Gradually whisk in the chicken broth, making sure there are no lumps. Bring to a simmer.
**Cook the Noodles:** Add the egg noodles, thyme, and rosemary to the pot. Simmer for 8-10 minutes until the noodles are tender.
**Add Chicken and Cream:** Stir in the shredded chicken and heavy cream. Let the soup heat through for 3-5 minutes. Season with salt and pepper to taste.
**Garnish and Serve:** Remove from heat and garnish with fresh parsley if desired. Serve hot with bread or crackers.