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1
Put a 13- by 9-inch shallow flameproof roasting pan (not glass) in middle of oven and preheat oven to 375u00b0F.
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2
Pat duck dry and trim off any excess fat. Score duck skin in a crosshatch pattern at 1/2-inch intervals with a sharp knife, then sprinkle with 1/2 teaspoon salt and 1/4 teaspoon pepper. Place duck, skin sides down, in roasting pan and roast until thermometer inserted diagonally into center registers 135u00b0F, 25 to 30 minutes for medium-rare.
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3
Preheat broiler. Turn duck over and broil (skin sides up) 6 inches from heat until fat is golden, 1 to 2 minutes. Transfer to a cutting board and let stand, loosely covered with foil, 10 minutes. (Internal temperature will rise to at least 145u00b0F.)
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4
While duck stands, pour off all but 2 teaspoons fat from pan, then add shallots and saute over moderately high heat, stirring, until golden brown, about 2 minutes. Add sugar and cook, stirring, until sugar is dissolved. Add vinegar, along with remaining 1/4 teaspoon each of salt and pepper, and cook, stirring and scraping up brown bits, 30 seconds. Transfer to a bowl, then whisk in oil until combined. Stir in walnuts.
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5
Thinly slice duck and serve with vinaigrette drizzled around plates.
