Heat the olive oil in a large pot or Dutch oven over medium heat. Add the chopped onion, carrots, and celery. Cook, stirring occasionally, until the vegetables begin to soften, about 6-8 minutes. Add the minced garlic and cook for another minute until fragrant.

Stir in the dried thyme and rosemary, and cook for about 30 seconds to toast the herbs and release their flavor.

Pour in the broth and add the diced tomatoes (with their juice), potatoes, and the bay leaf. Season with salt and pepper. Bring the mixture to a boil, then reduce the heat to low, cover, and let it simmer for 15-20 minutes, or until the potatoes are tender.

Add the shredded turkey, green beans, corn, and peas to the pot. Stir to combine and continue to simmer for another 5-10 minutes, just until the turkey and vegetables are heated through.

Remove the bay leaf before serving. Taste the soup and adjust the seasoning with more salt and pepper if needed. Ladle into bowls and serve hot.