Heat the olive oil in a large pot over medium heat. Add the ground turkey and cook, breaking it up with a spoon, until it is no longer pink.
Add the onion, carrots, and celery. Cook for about 5 minutes, stirring occasionally, until the vegetables begin to soften.
Stir in the garlic and cook for 1 minute until fragrant.
Add the barley, chicken broth, thyme, bay leaves, salt, and pepper. Bring the soup to a boil.
Reduce the heat to low, cover the pot, and simmer for 35 minutes or until the barley is tender.
Remove the bay leaves. Stir in the spinach and cook for 2 minutes until it wilts.
Ladle the soup into bowls and sprinkle with fresh parsley before serving.