Preparation

• 把醋和糖在宽2夸脱深saucepan and cook over high heat until the sugar dissolves and the mixture reduces to a syrup, 1 to 2 minutes. Add the stock and 1 cup of the grapefruit juice and cook over high heat, stirring occasionally, until reduced to about 3/4 cup, 20 to 30 minutes. Whisk in the cream and boil until the sauce reduces to about 1 cup, about 5 minutes. Set aside.
• Trim the duck breasts of excess skin and fat, and score the skin in a 1/2-inch crosshatch pattern, cutting almost but not quite through to the meat.
• In a small bowl, whisk 1 Tbs. of the remaining grapefruit juice with the honey and allspice. Brush the mixture all over the duck, working it down into the crosshatches. Season generously with salt and pepper, and set aside for at least 15 minutes. Position a rack in the center of the oven and heat the oven to 425°F.
• Heat a heavy-duty 12-inch skillet over medium-low heat. Put the duck in the skillet, skin side down, and cook, occasionally spooning off the excess fat as it renders, until the skin is very dark and much of the fat has rendered, 7 to 9 minutes.

• Flip the breasts, transfer the skillet to the oven, and roast until rare (125°F) or medium rare (135°F), about 5 to 8 minutes for small breasts or 8 to 12 minutes for large. Transfer the duck to a cutting board, cover loosely with foil, and let rest for about 5 minutes.
• Gently reheat the sauce, if necessary. Stir in the remaining 1 Tbs. grapefruit juice, and season to taste with salt and pepper. Slice the duck and serve with the sauce.

Make Ahead Tips

The sauce may be made 1 day ahead; cover and refrigerate until ready to serve.