Rinse the dried white beans, then place in a large bowl and cover with the 4 quarts water; soak 12β24 hours. Transfer the beans and soaking water to a large pot. Add the onion (peeled and studded with the whole cloves), the carrot pieces, smashed garlic, thyme sprigs, and bay leaves. Bring to a simmer over medium heat, then reduce to low and cook until the beans are just tender, 45β60 minutes. Drain, reserving the beans.
Heat the duck fat in a large skillet over medium heat. Add the pork shoulder and pork belly and brown on all sides, 8β10 minutes. Add the fresh garlic sausage pieces and brown until lightly colored, 4β5 minutes. Nestle in the duck confit legs, skin side down, and sear until the skin renders and crisps, 3β4 minutes. Transfer all meats to a tray.
Heat the oven to 325Β°F. Line the bottom of a 4β5 quart casserole with the pork rind strips. Spoon in half the cooked beans, arrange the browned meats evenly on top, then cover with the remaining beans. Pour in the unsalted chicken stock to just moisten the top layer. Season the surface evenly with the kosher salt and black pepper.
Bake, uncovered, until the cassoulet is bubbling and a crust forms on top, 2β2.5 hours. During baking, use the back of a spoon to break the crust down into the beans two or three times for a silky texture. Continue baking until the beans and pork shoulder are very tender and the top is richly browned.
Let the cassoulet rest for 15β20 minutes before serving so the juices settle. Serve hot from the casserole.