Place a small broiler pan or aluminum container directly below the rack on which you cook the duck pieces. This will allow you to catch the drippings and prevent barbecue flare-ups.
Preheat the barbecue to medium heat, with the central burner off, for indirect cooking.
Trim some of the excess skin from the ends of each breast and leg, then score the skin in a crisscross pattern, without cutting into the meat. Salt and pepper to taste. Place the duck legs, skin side down, on the barbecue rack over the unlit element. Grill 7-8 minutes, turn once and continue cooking, meat side down, about 75 to 90 minutes, with the lid closed. To finish cooking, turn skin side down once more and cook for 4 minutes or until meat comes off the bone easily.
Fifteen minutes before the legs are finished cooking, grill the breasts 3 minutes with the skin side down, then 9-10 minutes with the meat side down, and finish with another 3 minutes with the skin side down, or until an internal temperature of 58° C is reached (137° F). The breast should be moderately firm to the touch and still moist inside. Keep a close watch to prevent the barbecue from flaring up. If this happens, move the meat to a different spot and turn it over. Brush the legs and breasts with the pepper and sesame sauce in the last 5 minutes of cooking.
Grill the peppers on the barbecue at the same time as the duck, turning them a few times. Remove the food from grill and let rest for 5 minutes, loosely covered with a sheet of aluminum foil. Brush the duck pieces and grilled peppers with the chili and sesame sauce and serve in a large serving dish.
Chili and sesame sauce
Place all ingredients in a small saucepan and heat until the jelly dissolves. Remove from heat and use this sauce to coat the food when it is nearly finished cooking.
Recipe developed by Nicolas Vallée, professional chef