Heat a large pot over medium heat. Add the olive oil to the pot and follow with the minced onion, celery, and carrots. Cook until the trio of vegetables is tender and fragrant, about 10 minutes. Stir in the garlic and cook for another minute more.
Next, add the rice followed closely by the broth, water, herbs, and bay leaf. Bring to a boil, reduce to a simmer, and cook for 25 minutes. After that time, stir in the potatoes and green beans. Continue to cook until the rice and potatoes are just about tender then stir in the tomatoes, tomato paste, and chickpeas. Cook for another 5 to 10 minutes until everything is tender.
Finally, add in the salt and parmesan. Taste and adjust the seasoning as desired. I’ll often add a bit more parmesan before adding more salt (I like quite a bite of the parmesan in mine). Finish with a few cranks of black pepper and extra parmesan, if desired.