In a large pot or Dutch oven, melt the butter over medium heat.
Add the onion, carrots, celery, and garlic, and cook, stirring occasionally, for about 5 minutes until the vegetables soften.
Stir in the flour, salt, pepper, thyme, and oregano, and cook for another 2 minutes.
Add the chicken broth and diced potato, stir, then increase the heat to medium-high. Let the soup come to a boil, cooking for 3 minutes.
Reduce the heat to medium-low, partially cover the pot, and let the soup simmer for 25 minutes, or until the potatoes are tender.
Taste the soup, and adjust the seasoning if needed.
Add the shredded chicken, half-and-half or milk, and noodles, then cook for about 10 minutes until the noodles are tender and the soup has thickened.
Serve the soup warm. For leftovers, store covered in the fridge for up to a week. To reheat, warm in a pot over medium heat, adding a bit of chicken broth if it has thickened too much.