Preheat the oven to 300°F
Trim any excess fat around the cavity of the duck and remove the neck and giblets. Freeze for use in a future stock.
Pat the exterior and interior cavity of the duck dry. Using a sharp knife, score the skin on the breast in a crosshatch pattern, taking care not to cut through to the meat. Rub the salt all over the duck and inside the cavity, taking time to work it into every nook and cranny. Repeat this step with the pepper and place the duck, breast-side-up, on a v-rack inside a large roasting pan. Pop the duck into the oven and roast for 1 hour.
Once the first hour has elapsed, take the duck out of the oven and carefully flip it so it is breast-side-down. Return the duck to the oven and roast for another hour. Once the hour is up, reorient the duck so it is facing breast-side-up once again. Place it back in the oven and roast for 15 minutes more.
While the duck is roasting, pour the olive oil in a medium-sized skillet and place it over medium-low heat. Add the figs and let cook undisturbed until they begin to brown, about 5 minutes. Pour the port and honey over the figs and add the rosemary, bay leaves, allspice berries, peppercorns, and cinnamon stick to the pan. Bring the mixture to a rapid simmer, then reduce the heat to low. Let cook until the figs are jammy and most of the liquid has been absorbed.
Take the figs off of the heat and remove the bay leaves, rosemary, allspice berries, and cinnamon stick. Transfer the figs to a food processor and blitz until smooth. Transfer to a bowl and set aside to cool.
Once the duck has roasted for 15 minutes more, take the duck out of the oven and increase the oven temperature to 425°F. Once the temperature is up, place the duck back in the oven and roast for another 15 minutes or until the skin is golden.
Take the duck out of the oven and slather it liberally with the fig mixture. Return the duck to the oven and roast for another 5 minutes or until the duck appears shiny and glazed.
Let the duck rest for 10-15 minutes before carving.