Heat the olive oil in a large pot over medium heat. Add the onion, carrots, and celery. Cook for 5 minutes until the vegetables begin to soften.
Stir in the garlic and Swiss chard stems. Cook for 2 minutes more.
Add the diced tomatoes, vegetable broth, farro, oregano, salt, and pepper. Bring the mixture to a boil, then reduce to a simmer. Cover and cook for 25 minutes.
Stir in the cannellini beans and Swiss chard leaves. Simmer uncovered for 5 minutes until the greens wilt and the farro is tender.
Ladle into bowls and top with fresh basil leaves.