In a stock pot, heat oil over medium heat. Add in onion and cook until soft. Add carrots, celery and garlic and cook for an additional 3 minutes.
Next, mix in chicken broth, tomatoes, orzo (pasta), thyme, oregano, rosemary and stir to combine. Bring soup to a simmer, stirring occasionally. Simmer for 10 minutes, stirring occasionally, until the pasta is tender.
Add in the spinach and cook for 1-2 minutes until it is bright green and wilted. Season with salt and black pepper to taste (if needed). Serve warm. Serves 4-6.