Heat the olive oil in a large pot over medium heat. Add the onion, carrots, and celery and cook for 5 minutes until the vegetables begin to soften.
Stir in the garlic and cook for 1 minute more.
Add the pearl barley and vegetable broth. Bring the mixture to a boil, then reduce the heat to low and simmer uncovered for 25 minutes.
Stir in the zucchini and continue simmering for 10 minutes until the barley is tender.
Add the spinach, parsley, and thyme. Cook for 2 minutes until the spinach wilts.
Season with salt and pepper to taste before serving.