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Preheat oven to 400 F.
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Score the skin of duck breasts in parallel lines or in criss-cross pattern. Generously season both sides of duck breasts (and especially add more salt to the skin side!) with at least 1/2 teaspoon salt.
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Use a large oven-proof cast iron pan, or use an oven-proof large stainless steel skillet (make sure that the pan you use has an oven-proof handle).
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Heat 1 tablespoon of olive oil in a large skillet on medium heat until the oil is hot. Add duck breasts to the skillet skin side down.
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Cook the duck breasts, uncovered, for about 8 minutes on medium heat on the skin side, until the fat is released. I like to use a splatter screen to keep the oil from splattering (the splatter screen allows the heat to escape). After 8 minutes, remove the duck fat from the skillet, leaving just enough to cover the bottom of the skillet. Turn the duck breasts over to the other side (non-skin side) and cook for 2 more minutes on medium heat.
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Place your oven proof skillet (with duck breasts in it) in the oven (preheated to 400 F) and let the duck breasts roast for about 5 minutes, until they are medium rare.
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Remove the skillet from the oven (wearing oven-proof gloves to protect your hands, of course), and let the duck breasts rest for about 7 minutes before slicing them.