Heat the oil and butter over medium heat in a 3-quart saucepan; add the onions, celery, and garlic. Saute until the vegetables are softened but not browned, about 6-8 minutes.
Add the beans, cheese rind, stock/water and salt and bring to a boil. Reduce heat, partially cover and simmer for 20 minutes.
Add the broccoli, and simmer 3 to 5 minutes, until just cooked. Just before serving, stir in the balsamic vinegar and season with freshly ground black pepper to taste. Serve the soup with grated Parmigiano cheese, if desired.