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1
To cook the duck, preheat the oven to 325F.
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2
Heat a grill pan over high heat.
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3
Season the duck legs with salt and pepper on both sides and brush with 3/4 cup of the barbecue sauce.
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4
Grill the legs until golden brown, 3 to 4 minutes on each side.
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5
Put the stock in a medium roasting pan, add the remaining 1/2 cup barbecue sauce, the onion, ginger, cloves, star anise, cinnamon sticks, fennel seeds, and black peppercorns and season with salt.
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6
Arrange the duck legs in the pan, cover with foil, and braise in the oven until the meat is tender and falling off the bone, 1 1/2 to 2 hours.
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7
Meanwhile, make the coleslaw.
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8
Whisk together the mayonnaise, mustard, vinegar, celery seeds, and celery salt in a large bowl.
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9
Add the cabbage, carrot, and onion, season with salt and pepper, and toss well to combine.
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10
Cover and refrigerate for at least 30 minutes and up to 4 hours before serving.
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11
Transfer the duck to a platter and tent loosely with foil.
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12
Skim off any fat from the liquid; then strain the liquid into a bowl.
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13
Pour 2 cups of the braising liquid into a large saute pan and boil over high heat until reduced to 1 cup, 8 to 10 minutes.
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14
Shred the duck into bite-sized pieces, add to the reduced sauce, and toss to combine.
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15
Mound the duck onto the bottoms of the buns, top with some of the coleslaw and a few pickle slices, if desired, and cover with the tops.
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16
Serve extra pickles on the side.
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17
Bring the vinegar, garlic, jalapeno, sugar, and salt to a simmer in a saucepan over high heat and cook until the sugar dissolves, about 1 minute.
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18
Remove from the heat, add the dill, and let cool to room temperature.
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19
Place the cucumbers in a small container with a lid, pour the vinegar solution over them, and stir to combine.
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20
Cover and refrigerate for at least 2 hours and up to 2 days before serving.