Heat olive oil in a large pot or Dutch oven over medium heat. Add onion, carrots, and celery and cook until softened, about 5-7 minutes.
Add vegetable broth, diced tomatoes, green beans, oregano, salt, and pepper. Bring to a boil, then reduce heat and simmer for 20 minutes.
Add pasta and continue to simmer until pasta is tender, about 10-12 minutes.
Stir in spinach and cook until wilted, about 2 minutes.
Serve hot, garnished with grated Parmesan cheese.