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 sliced mushrooms and cook for another 4 minutes until they release some liquid and start to brown.
Add the quick-cooking barley, vegetable broth, and dried thyme. Bring the mixture to a boil, then reduce to a simmer.
Cover and cook for 15 minutes, stirring once or twice, until the barley is tender.
Stir in the fresh spinach and cook for 2 minutes until it wilts. Season with salt and black pepper to taste.
Ladle into bowls and top each serving with chopped fresh parsley.