Layers of ingredients yield layers of flavor in this iconic casserole from southwestern France. From start to finish, this dish takes about 18 hours to prepare, although most of it is unattended.
Bundle parsley, bay leaf, rosemary, thyme, celery, and leek to form a bouquet garni, wrapping kitchen twine around the aromatics several times to secure -- which ensures easy retrieval of the ingredients after they've infused the cooking liquid with flavor.
Warm oil in a large pot over medium heat. Add fatback or pork belly, and cook until it is golden on all sides and has begun to render its fat, about 5 minutes. Add pork shoulder, and cook until golden on all sides, about 8 minutes total.
Stick clove in half the onion, and add to pot along with bouquet garni, ham hock, carrot, tomatoes and juice, and beans. Add enough cold water to cover by 1 to 2 inches (about 8 cups). Bring to a boil. Reduce heat, and simmer gently until beans are tender throughout but not falling apart, 40 to 50 minutes.
Remove pot from heat. Discard carrot, onion, and bouquet garni. Transfer ham hock to a cutting board, reserving liquid, and let cool slightly. Trim meat and gelatin from the bone, dicing and returning them to the pot. Discard the bone.
Preheat oven to 300 degrees. Rub cut side of garlic clove over the entire inner surface of a small (5-quart) Dutch oven or other ovenproof vessel. This allows a subtle though distinct garlic flavor to infuse the resulting cassoulet.
Using a wire skimmer or a slotted spoon, place half the bean mixture in the Dutch oven, spreading it evenly. Leave the cooking liquid in the pot.
Arrange the duck confit and sausage on top of the beans in the Dutch oven to create a single, snug layer. Spoon the remaining beans over the meat, reserving the cooking liquid.
Add enough cooking liquid so the beans are almost, but not quite, submerged. Reserve the remaining liquid. Transfer pot to oven and cook, uncovered, for 2 hours. Check the liquid every 30 minutes to make sure it is no more than 1/2 inch below the beans, and add liquid or water as necessary. Do not stir.
After the cassoulet has cooked for 2 hours, toss bread and butter in a bowl. Sprinkle over cassoulet, and return to oven until beans are tender and bread is golden, 1 to 1 1/2 hours.
Before serving, let cassoulet stand at room temperature for 20 minutes to cool and to allow the beans to absorb some of the liquid. You can refrigerate cassoulet in an airtight container for up to 3 days; rewarm in an oven heated to 300 degrees.