Use a sharp knife to score the skin side of the duck breasts in 2 directions, about 20 slashes per direction. Season the breasts on both sides with salt and pepper. Reserve in the refrigerator.
Cut off 1 end so the orange can stand on the cutting board, and slice off 2 (2-inch) strips of zest. Cut the zest into fine julienne, then blanch the zest for 1 minute in the cup of boiling water. Juice the orange, strain the juice into a saucepan, and boil it until it's reduced to about 1 tablespoon.
If you're using the kumquats instead, cut the round ends off the kumquats and eat or discard them. Set the kumquats on 1 end and use a sharp paring knife to trim the zest off three of them. Cut all the kumquats in half lengthwise, and working over a strainer set in a non-reactive bowl, remove the pulp with a small spoon. Push the pulp against the strainer to extract the juice. (Don't worry if you end up with only a tablespoon or 2.) Place the kumquat zests on a cutting board and slice them into fine julienne. Bring the 1/2 cup water to a boil over high heat, blanch the zests for 1 minute, then drain them in a strainer.
If you're using concentrated duck broth, reduce it in a small saucepan to about 2 tablespoons until it's lightly syrupy.
Heat a saute pan over medium to high heat and saute the duck breasts, skin side down, 8 to 10 minutes for the Pekin duck breasts and 12 to 18 minutes for the mallard. Turn the breasts over, adjust the heat to high, and cook for 1 minute for the Pekin duck and 2 minutes for the mallard.
Pour the fat out of the pan – if it hasn't burned, save it for omelets – and deglaze the pan with the reduced kumquats or orange juice. Use a whisk to add the glaze. Add the sugar, Grand Marnier, kumquat or orange zest, and vinegar, and simmer the sauce for about 30 seconds to cook off the alcohol. At this point, adjust the thickness of the sauce – its consistency is up to you, but many cooks make their sauces too thick; add 1 or 2 teaspoons water to thin it or simmer the sauce for a moment to reduce and thicken it. Whisk in the cold butter, keeping the pan and whisk moving until all the butter melts. (Don't let it sit without whisking or the butter will separate.) Season, to taste, with the pepper, and if necessary, a few more drops of vinegar.
Slice the breasts crosswise, arrange the slices on individual heated plates, and spoon the sauce over the breasts. Serve hot, with orange wedges if desired.
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