Melt 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, stirring.
Add chicken broth and diced potato. Stir. Bring to a boil, stirring occasionally, for 3 minutes, then reduce to a simmer. Cover partially and cook for 25 minutes, or until potato is soft. Taste and adjust seasoning if needed before adding the chicken and noodles.
Stir in chicken, milk/half-and-half, and noodles. Cook uncovered for 10 minutes, stirring occasionally, until noodles are tender and the soup thickens.
Taste, adjust seasoning, and if desired, add a squeeze of fresh lemon. Garnish with fresh thyme if using. Serve hot with crusty bread or a side salad.