In a large 8 quart pot, heat oil, onion and garlic together and cook until soft. Add carrots, celery, potatoes, 2 cups of beans, 4 cups of bean cooking liquid (or water) and basic tomato sauce and bring to a boil. Lower heat, add chard, kale, black cabbage and simmer 1 1/2 hours until everything is soft. Add remaining beans and adjust seasoning. Allow to cool and rest overnight.
The following day, bring to a boil and serve in shallow bowls over toasted bread. Sprinkle with parmigiano tableside.