Sauté the vegetables: Heat the olive oil and butter in a large soup pot over medium heat. Add the onion, celery, and carrots. Cook until softened and fragrant, about 6–7 minutes.
Add the garlic: Stir in the minced garlic and cook for 30 seconds.
Season and add broth: Pour in the chicken broth. Add the thyme, rosemary, sage, oregano, and turmeric. Stir well.
Simmer the base: Bring the soup to a gentle boil, reduce the heat, cover, and simmer for 20 minutes so the flavors come together.
Add the chicken: Stir in the cooked shredded chicken and let it warm through.
Cook the noodles: Add the noodles directly into the pot and simmer until tender, about 6–10 minutes depending on the shape. Add more broth if needed.
Season to taste: Finish with salt and pepper until it tastes just right.