Sear. Heat your skillet with the duck breast portions over low heat for the first 3 minutes. Then, increase the heat to medium. Once the duck breast is sizzling and the fat is starting to render off, leave the duck breast undisturbed. Continue to sear with the fat side down to cook for an additional 6 to 8 minutes. Then, drain or spoon off excess duck fat from your skillet.
Oven finish. To finish your duck breasts in the oven, either make sure your skillet is oven-safe or preheat a clean, rimmed baking sheet at 400°F (205°C) while starting your duck portions in your skillet. When ready, transfer your duck breasts to your baking sheet with the skin side down and roast in the oven for an additional 4 to 6 minutes.