In a colander, rinse the beans and pick out any debris or small stones.
In a medium stockpot, add rinsed beans and cold water to cover the beans by about 2 inches. Cover and soak overnight.
Drain the beans and cover them with fresh water. Add the Parmesan cheese rind. Over medium heat, simmer until the beans are tender, about 30 minutes. Set aside.
In a large Dutch oven over medium heat, add ½ cup olive oil, diced onions, carrots, and celery (soffritto). Cook, stirring occasionally until the onions are translucent, for about 10 minutes.
Stir in tomatoes, beans, and their cooking liquid. Season with salt, pepper, and oregano. Add the chard and cabbage. Note: Add additional water, chicken or vegetable broth as needed to completely cover the chard and cabbage.
Bring the mixture to boil. Reduce the heat and simmer for 1 hour. Adjust the seasonings to taste.
Place a piece of bread in each bowl. Ladle the soup on top of the bread. Top each serving of the soup with Parmesan cheese, a dash of olive oil, and freshly ground black pepper.