Cover dried beans with water and soak for 6-8 hours. Once soaked, drain beans and set aside.
Over medium heat, warm olive oil in a 6-quart stockpot or Dutch oven. Sauté the carrot, celery, and onion with salt and pepper. Sauté until the onion is translucent, 5 minutes.
Add soaked beans, ham bone, Parmesan rind, and chicken stock. Bring to a boil and reduce to a simmer. Cook until the beans are tender, 2-4 hours.
Once the beans are tender, remove the Parmesan rind and ham bone. Allow the beans to rest for 20 minutes so the liquid will continue to thicken. Remove any meat from the ham bone and add back to the beans. Alternatively, more ham can be added. Adjust beans for salt to taste and serve with cornbread.