The day before you plan to serve the cassoulet, pick over the beans and cast aside any stones, grit, bits of twigs, or other curious objects you find. Rinse the beans in a colander and drain them well. Dump the beans in a bowl and add enough water to cover by at least 3 inches. Let soak overnight.
The next day, cut the duck into 8 pieces and trim off all visible fat and excess skin, reserving both the duck pieces and the excess duck fat and skin.
Cook the duck fat and skin in a large heavy skillet over medium heat until between 1/4 and 1/3 cup fat has rendered and is shimmering, golden and beautiful, about 4 minutes.
Remove and discard the solid pieces of fat and skin. Season the duck and lamb with the salt and pepper. Add the duck pieces to the skillet and sear them in the hot fat, turning to brown both sides. Transfer them to a plate. Repeat with the lamb cubes and then the sausage chunks.
Scatter the onion and celery into the skillet and sauté until lightly browned. Add the garlic, Italian seasoning, nutmeg, and cloves and sauté until aromatic, about 1 minute. Add the wine and bring to a boil. Add the chicken stock or broth and tomatoes and bring to a boil. Remove from the heat.
Drain the beans. In a 6-quart slow cooker with an ovenproof insert (check the manufacturer's instructions), layer the beans and meats, beginning and ending with the beans and alternating with the meat (4 layers of beans, 3 of meat). Pour the hot stock mixture over the layers of beans and meat. Cover and cook until the beans are tender, 8 to 10 hours on low. (We found that 9 hours did the trick perfectly.)
Crank the oven to 350°F (180°C).
Mix the bread crumbs and parsley in a small bowl and scatter over the top of the cassoulet. Remove the insert from the slow cooker, place it on a baking sheet, and bake until the top of the cassoulet is browned and bubbling, about 30 minutes. Serve immediately. (You can cover and refrigerate the cassoulet for up to 5 days. Reheat gently in a low oven or on the stovetop over low heat.)