Sauté vegetables: In a large pot, melt butter with olive oil. Add onion, carrots, celery, and garlic. Cook for 5–7 minutes until softened.
Make the roux: Stir in flour and cook for 1–2 minutes, stirring constantly to remove the raw flour taste.
Add broth: Slowly pour in chicken broth while stirring to avoid lumps. Bring to a gentle simmer.
Add chicken and noodles: Add shredded chicken and egg noodles. Simmer for about 8–10 minutes, until noodles are tender.
Add cream: Reduce heat and stir in milk or cream. Let the soup simmer gently for another 3–5 minutes until creamy and thickened.
Season and serve: Stir in thyme, salt, and pepper. Garnish with chopped parsley and serve warm.