Place the beans in a large Dutch oven or stockpot, cover the beans with plenty of water, about 2” over and let them soak overnight. Drain the water and set the beans aside while you sauté the vegetables.
In the same Dutch oven, melt 2 tablespoons of the butter with the olive oil over medium heat. Add the onions, carrots, and celery, cooking until the vegetables are very tender, about 15 to 20 minutes. Add the garlic and cook for 3 minutes.
Return the beans to the stockpot along with the stock and dried rosemary. Bring to a boil over medium heat, partially cover and cook for about 45 minutes to an hour or until the beans are mostly tender. While the beans cook, make the mashed potatoes.
Place the potatoes in a medium saucepan, cover with water and add 1 tablespoon of the kosher salt. Bring to a low boil over medium heat, partially cover and cook for about 30 to 40 minutes or until the potatoes are fork tender.
Drain the water from the potatoes then add the remaining 2 tablespoons butter along with the nutmeg, ½ teaspoon kosher salt, ¼ teaspoon black pepper, and the half and half. Mash the potatoes until mostly smooth.
When the beans are tender add the remaining kosher salt, black pepper, and concentrated cooking stock. continue to cook for another 30 minutes until the beans are cooked through and very tender.
Stir in the mashed potatoes, blending them into the soup. Toss in the chicken and cook until heated through.
Serve with a sprinkling of Parmesan cheese.