Heat the Oil: In a large pot, heat the olive oil over medium heat. Add the diced onion, minced garlic, sliced carrots, and sliced celery. Sauté for about 5 minutes, until the vegetables are softened.
Add Broth and Seasonings: Pour in the chicken or turkey broth. Add the bay leaf, dried thyme, salt, and pepper. Bring the mixture to a boil.
Cook Noodles and Turkey: Once the broth is boiling, add the long noodles and cook according to the package instructions, usually about 8-10 minutes, until al dente. In the last 5 minutes of cooking, add the shredded or diced leftover turkey to the pot to heat through.
Finish and Serve: Remove the bay leaf. Taste and adjust seasoning if necessary. Ladle the soup into bowls and garnish with fresh chopped parsley if desired. Serve hot.