Melt the butter in a Dutch oven or large pot set over medium heat. Add in the diced onions, carrots, celery, and parsley; cook for 5 minutes, stirring occasionally. Stir in the garlic; cook for 20 seconds.
Add in the flour, salt, oregano, thyme, and black pepper, and cook for 3 minutes, stirring frequently. Stir in the chicken broth, scraping up all the browned bits from the bottom of the pot.
Add in the bay leaves and chicken breasts, and bring to a boil.
Reduce heat to a steady simmer; partially cover with a lid and simmer for about 20 to 25 minutes, or until the chicken is cooked through and no longer pink inside.
Remove the cooked chicken breasts from the soup and transfer them to a cutting board; let cool for a couple of minutes, then shred the meat. Return the shredded chicken to the pot.
Stir in the milk, heavy cream, and noodles; bring to a steady boil and cook for about 7 minutes or until noodles are cooked al dente.
Remove from heat and discard the bay leaves.
Taste the soup for salt and pepper, and adjust accordingly.
Ladle into bowls and serve.