In a small saucepan or skillet over medium-low heat, heat the bean broth and vegetable broth.
In a soup pan over medium heat, warm a good layer of olive oil. Sauté the onion and celery until soft, about 10 minutes.
Add the garlic and a pinch of salt; cook until softened, about 5 more minutes.
Add the parsley, rosemary, chile flakes, and tomatoes; cook for a few minutes.
Add the Swiss chard and a little bit of water to loosen the mixture as needed; cover and cook until the greens wilt, about 5 minutes.
Add the warmed broth to the soup. Add the beans and Parmesan rind; bring to a simmer.
Add the bread cubes to the soup, and a good pour of the remaining olive oil; stir well and cover the pan to dissolve the stale bread.
Reduce heat to low; cook for 30 minutes, checking liquid levels regularly.
Taste for salt and add a final pour of olive oil. Remove the Parmesan rind.
Serve the soup in bowls topped with black pepper and freshly grated Parmesan cheese.
