For the duck:
1 large duck, about 6 lbs., at room temperature
Kosher salt and freshly-ground black pepper, to taste
For the salad:
1 clove garlic, finely grated
1 tbsp. Dijon mustard
1 tsp. honey
¼ cup red-wine vinegar
¼ cup olive oil
4 cups torn radicchio leaves
½ cup roasted hazelnuts
½ cup sweet, mild olives, like Castelvetrano
¼ cup finely chopped flat-leaf parsley
Good bread, for serving
1. Make the duck: heat the oven to 250 degrees. Using a pair of poultry shears or a sharp knife, trim excess skin and fat from the neck and back cavity of the duck. There will probably be a fair amount; trim anything that overhangs (discard the trimmings or reserve them in an airtight container in the freezer to render for duck fat later). Pat the duck dry with paper towels, then generously sprinkle kosher salt inside the cavity. Using the tines of a sharp fork or the point of a sharp paring knife, prick the duck 15-20 times on each side, piercing through the skin and into the fat, but not so far to cut into the muscle beneath.
2. Set the duck, breast-side up, on a rack set inside a roasting pan, then transfer it to the heated oven. After an hour, open the oven, make a few more pricks on the top side of the duck using your fork or paring knife (the cooking process will have caused some of your original cuts to close), flip the duck breast-side down, then make a few more pricks on the upward face. Continue roasting for another hour, then flip the duck again. Repeat this process, flipping each hour until the bird has cooked for four hours total. Finally, remove the bird from the oven and raise the heat to 350 degrees. While the oven is coming to temperature, carefully remove any fat and juices that have accumulated in the bottom of the roasting pan. Reserve ¼ cup (the remaining fat and juices can be saved for another use). Return the duck to the oven, breast-side up, for an additional 30-45 minutes, flipping halfway through. When the skin is crisp and golden, remove the duck from the oven, sprinkle it gently with salt and pepper and let it rest for 15 minutes while composing the salad.
3. Make the salad: in a small jar or bowl, whisk together the grated garlic, mustard, honey, vinegar, olive oil, ¼ cup reserved duck fat (or more olive oil, if not enough duck fat is on hand) and a pinch of salt. Taste the mix, adjusting for salt, if necessary. The dressing should be quite fiery. In a large bowl, toss the radicchio with just enough of the dressing to coat the leaves, then transfer the salad to a serving platter. Using a mortar and pestle or the bottom of a heavy skillet, roughly crush the hazelnuts. Using your hands, tear the olives in half, removing any pits (this makes a nice ragged texture, but chopping them is fine, too). Scatter the nuts and olives across the greens and drizzle on additional dressing.
4. When the duck is rested, have someone else carve it. Arrange the duck pieces atop the dressed salad, pour a few spoonfuls of the reserved drippings over the meat and finish it with a flurry of chopped parsley. Serve with good bread and many napkins.