Melt the butter in a large pot over medium heat. Add onion, carrots, celery, and garlic. Cook for 5 minutes until softened.
Stir in flour, salt, pepper, thyme, and oregano. Cook for 2 minutes.
Add chicken broth and diced potato. Increase heat to medium-high and bring to a boil. Boil for 3 minutes.
Reduce heat to medium-low, partially cover, and simmer for 25 minutes until potatoes are tender.
Add cooked chicken, milk, and noodles. Cook for 10 minutes until noodles are tender and the soup thickens.
Taste and adjust seasoning. Serve warm.