In a large, heavy-bottomed pot over medium heat, melt butter. Then add onion, carrots, and celery. Sweat the vegetables for 5 - 6 minutes, stirring occasionally, until they begin to soften. Add garlic and stir to combine.
Sprinkle flour over vegetables. Then add salt, pepper, dried thyme, and bay leaves. Stir to combine, making sure the flour coats the vegetables. Cook for a minute or two.
Add chicken stock, increase heat to medium high. Give it a good stir, making sure to scrape the bottom of the pot to release any flour that may have stuck. Reduce heat to medium low, and cover the pot with a lid slightly ajar to allow some steam to escape. Simmer for 20 - 25 minutes. *Keep on eye on the pot. If it begins to boil, reduce the heat - you want a gentle simmer. Remove lid from the pot, and add chicken, corn, green beans, and noodles. Simmer for an additional 8 - 10 minutes. Discard bay leaves.
Turn off the heat, and add half and half (or milk). Stir to combine, and taste to adjust seasonings, if needed. Garnish with fresh dill and/or fresh parsley if desired, before serving.