Heat the olive oil in a large pot over medium heat. Add the diced onion, carrots, and celery, cooking for about 5 to 7 minutes until the onions are translucent and the vegetables begin to soften. Stir in the minced garlic and cook for another minute until it becomes fragrant, being careful not to let it brown.
Add the cubed turkey breast to the pot. Cook the turkey until it is browned on all sides, which usually takes about 5 minutes. If you are using pre-cooked leftover turkey, you can skip this browning step and simply move on to adding the liquids.
Pour in the chicken broth and the diced tomatoes with their juices. Stir in the green beans, thyme, and rosemary. Bring the mixture to a gentle boil, then reduce the heat to low. Cover the pot and let it simmer for 20 minutes to allow the flavors to meld and the vegetables to become tender.
Once the soup has simmered, stir in the fresh baby spinach. The heat from the soup will wilt the spinach in about 1 to 2 minutes. Taste the soup and add salt and black pepper as needed. Remove the pot from the heat and let it sit for a few minutes before serving.
