Heat the olive oil in a large Dutch oven over medium heat. Add the onion, carrot, and celery; stir often for 2 minutes. Add the minced garlic and cook, stirring constantly, for 1 minute. Add the broth and leftover turkey then season with sea salt and freshly cracked pepper, to taste (if needed). Cover with a lid and let the soup simmer for 30-40 minutes, stirring occasionally.