Heat olive oil in a large pot over medium heat. Add onion and cook until translucent. Add garlic and cook until fragrant, 30 seconds. Add carrot, celery, tomatoes, zucchini, and potatoes. Cook eight to 10 minutes, stirring often, until very soft and lightly golden. Stir in tomato paste and season with bay leaves, oregano, salt, and pepper.

Stir well. Add broth and bring to a gentle boil. Stir in the beans and cook until soft, about 20 minutes. Add arborio rice and cook an additional 20 to 25 minutes, stirring occasionally. The soup should thicken slightly but remain brothy.

Remove bay leaf. Add parsley, and stir. Cook another two to three minutes and serve hot.