Heat olive oil in a large pot over medium heat. Add onion, carrots, and celery. Sauté for 5-7 minutes until vegetables are tender.
Add garlic and cook for 1 minute until fragrant.
Stir in butter until melted, then whisk in flour to create a roux. Cook for 2 minutes, stirring constantly.
Gradually whisk in chicken broth, ensuring no lumps form. Bring to a simmer.
Add thyme, bay leaf, salt, and pepper. Stir in egg noodles and cook for 8-10 minutes until tender.
Add cooked chicken and heavy cream. Simmer for 5 minutes, stirring occasionally. Remove bay leaf.
Taste and adjust seasoning if needed. Serve hot, garnished with fresh parsley.
Notes
For a lighter version, substitute half-and-half or whole milk for the heavy cream. Store leftovers in an airtight container in the refrigerator for up to 3 days.