Heat the olive oil in a large pot over medium heat. Add the diced onion and sauté for 3-4 minutes until it becomes translucent.
Add the minced garlic, sliced carrots, and sliced celery to the pot. Cook for an additional 5 minutes, stirring occasionally.
Pour in the turkey broth and bring the mixture to a boil.
Once boiling, add the shredded turkey, chopped green beans, dried thyme, and dried rosemary. Season with salt and pepper to taste.
Lower the heat and let the soup simmer for 30 minutes, allowing the flavors to meld.
If you choose to add egg noodles or rice, stir them in during the last 10 minutes of cooking to allow them to cook through.
Taste and adjust seasoning if necessary before serving. Use a ladle to serve the soup in bowls.