Heat olive oil in a large pot over medium heat.
Add diced onion and sauté until translucent, about 5 minutes.
Stir in minced garlic, diced carrots, and celery; cook for another 3-4 minutes.
Add diced tomatoes and cook for 2 minutes, letting the mixture simmer.
Pour in the broth, then add the cannellini beans and dried oregano; stir well.
Bring the mixture to a gentle boil, then reduce to a simmer and cover for 15 minutes.
Add the pasta and continue to simmer for another 10 minutes.
Stir in the fresh spinach just before serving, allowing it to wilt.
Taste and season with salt and pepper as needed before serving.