You only need 30 minutes of prep time and five ingredients to make this decadent holiday main. But plan ahead: You'll need over eight hours for marinating and resting.
Using a sharp knife, score the skin on each duck breast in a 3/4-inch crosshatch pattern, cutting almost to the meat. Season generously with salt and pepper. Transfer to an airtight container. Refrigerate for at least 8 hours or up to 1 day. Let the duck sit at room temperature for 30 minutes before cooking. Pat the duck dry with paper towels.
Preheat the broiler. In a large heavy broiler-proof skillet, arrange the duck breasts, skin-side down, and heat over medium. Add the star anise. Cook until the fat is almost completely rendered, about 15 minutes. Turn the duck breasts over. Spoon off all but 1 tbsp. of the duck fat from the skillet. (Reserve the fat for another use.) Cook the duck until an instant-read thermometer inserted horizontally into the thickest part of a breast registers 135° for medium-rare, 3 to 5 minutes. Transfer to a cutting board. Let rest for 5 minutes.
Add the grapes and shallots to the skillet and toss until coated in the duck fat; season. Broil, turning once, until the grapes and shallots are charred in spots, about 5 minutes. Remove the skillet from the broiler. Stir in the vinegar. Discard the star anise. Season the sauce.
Slice the duck breasts and arrange the meat on the plates, skin-side up. Top with the grapes and shallots. Drizzle with the sauce from the skillet.
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