How to Make It
Using poultry shears, cut the duck in half lengthwise: cut along both sides of the backbone and through the breast bone; remove the backbone. Cut each half into 2 pieces so that you have 2 legs and 2 breasts with wings attached. Alternatively, have your butcher do this.
Heat a large skillet. Add the duck pieces, skin side down, sprinkle with the salt and cook over high heat for 5 minutes. Lift the pieces so they don't stick, leaving them skin side down. Add the duck neck and gizzard to the skillet and cover tightly. Reduce the heat to low and cook until the duck skin is very brown, about 15 minutes. Turn the heat down to very low, cover and cook until the duck is tender, about 25 minutes. Add the liver and heart to the pan, and cook covered for 5 more minutes.
Transfer the duck legs, breasts, liver and heart to a large platter and keep warm in a low oven; discard the neck and gizzard. Pour the rendered duck fat into a small bowl and reserve for another use, setting aside 1 tablespoon for the dressing on the Green Salad. Add 1/4 cup of water to the juices in the skillet and stir to dissolve them.
If you'd like crisper duck skin, preheat the broiler. Arrange the duck legs and breasts, skin side up, on a broiling pan and broil until the skin is crisp. Transfer to plates along with the liver and heart and spoon half the reserved juices over the duck. Reserve the remaining juices.