Heat the olive oil in a large pot or Dutch oven over medium heat.
Add the diced onion, carrots, and celery. Sauté for about 5-7 minutes, or until the vegetables are softened.
Stir in the minced garlic, thyme, and rosemary, cooking for another 1-2 minutes until fragrant.
Pour in the turkey stock (or chicken stock) and bring the mixture to a boil.
Once boiling, add the shredded turkey, peas, green beans, and corn. If using, add the cooked noodles or rice at this point.
Reduce the heat to low and let the soup simmer for 30 minutes. Stir occasionally.
Season with salt and pepper to taste.
Serve hot, and enjoy your comforting bowl of leftover turkey soup!