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1
Score duck skin almost all the way through the skin and fat each way on the diagonal in a crosshatch pattern. Generously season with salt and rub salt into each breast. Let rest, skin-side up, at room temperature, for 15 minutes.
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2
Whisk chicken broth, orange liqueur, sherry vinegar, orange marmalade, orange zest, and cayenne pepper together in a small bowl.
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3
Pat duck breasts dry with paper towels. Re-season skin-side of duck breasts with salt.
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4
Heat duck fat in a heavy skillet over medium heat for 2 minutes. Place duck in skillet, skin-side down, and cook for 6 minutes. Flip duck breasts and cook until they start to firm and are reddish-pink and juicy in the center, about 4 minutes more. An instant-read thermometer inserted into the center should read 140 degrees F (60 degrees C). Transfer breasts to a plate to rest. Pour any rendered duck fat into a glass jar.
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5
Return skillet to medium heat and whisk flour into pan; cook and stir until flour is completely incorporated, about 1 minute. Pour orange mixture into skillet; bring to a boil. Cook until sauce thickens and is reduced, 3 to 5 minutes. Reduce heat to low. When orange mixture stops bubbling, add butter; stir until butter is completely melted and incorporated into the sauce, about 1 minute. Season with salt to taste.
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6
Slice duck breasts across the grain, arrange on a plate, and spoon orange sauce over the top.
