If you plan on having duck offal, make it easy on yourself and go all the way by cooking the trifecta of fowl organ meat -- the heart, liver and kidneys -- at the same time for simplicity. Although the heart, liver and kidneys cook at different rates, you can cook and serve them at the same time if you add them to the pan in descending order of cooking times, or heart first and kidneys and liver second. Cutting the heart in half, if it's a relatively large one, can cut down on cooking time.
Trim the liver and kidneys of any visible connective tissue and prick out any visible veins with the tip of a paring knife. Cut the white crescent of fat from the tops of the hearts, then slice the hearts in half if they're wider than 1 inch.
Bring a stockpot of water to a rolling boil. Fill a container with ice cubes and cover them with cold water while the water comes to a boil.
Add the heart, liver and kidneys to the water and blanch them for 3 minutes. Skim the froth from the surface of the water as it appears, then retrieve the duck parts with a slotted spoon and plunge them in the ice water. Chill the heart, liver and kidneys for 3 minutes, adding ice as needed.
Drain the heart, liver and kidneys and pat them dry with a kitchen towel. Cover the bottom of a saute pan with stock and bring it to a simmer over medium heat.
Add the duck heart and cover. Simmer the duck heart until the stock evaporates, about 5 or 6 minutes.
Add a few tablespoons of oil to the pan and coat the heart in it. Let the oil heat until sizzling.
Add the liver and kidneys when the oil starts sizzling. Season the heart, liver and kidneys to taste with kosher salt and freshly ground black pepper and give everything a quick toss in the pan to coat.
Saute the heart, liver and kidneys until golden brown on all sides, about 5 or 6 minutes. Check the doneness by slicing a kidney and liver in half. Fully cooked livers and kidneys have no traces of pink, and the juices run clear from them. The heart will be fully cooked after steaming, so you don't need to cut into it.
Add about a splash of stock or wine to the pan and scrape it with a wooden spoon to lift the fond, or caramelized bits, that stick to the bottom.
Transfer the heart, liver and kidneys to the serving plate and pour the pan juices over them.