Rinse the beans. Soak overnight in water 2 inches or so above the beans. Put the beans, vinegar, and about a cup of the olive oil in a large pot.
Add water to about an inch over the beans and bring them to a boil for 10~15 minutes. Turn down to simmer and cover with a lid. Check periodically to ensure the beans are still covered. They will take an hour or two, possibly longer. They should cook until they are holding together, but buttery soft inside.
In a large skillet over medium-high heat, add ¼ inch olive oil, the olives, and the onion. Cook about 2 minutes then add the garlic, peppers, carrots, herbs, salt, and coarse black pepper (2 teaspoons or so – or about 20 grinds from a pepper mill). Sauté until bubbling, then turn down to medium and cook for about 15 minutes.
When the beans are ready, add in the contents of the skillet. Stir into the beans. Add another glug of olive oil. They can simmer a while; they'll only get better.
Serve with the Parmesan cheese. Enjoy!