Heat the oil in a large stockpot on medium heat. Add the in the onion, celery & carrot; sauté for about 5-6 minutes until starting to turn tender.
Stir in half the Cannellini beans along with the tomatoes, greens, stock & rice. Bring to a boil, reduce to a simmer & cover for about 25-30 minutes until the vegetables are tender & the rice is cooked through. Stir in the remaining beans & simmer for another 3-5 minutes.