Instructions

Make the sauce

• Melt the butter in a 2-1/2- to 3-quart saucepan over medium heat until the foam subsides. Add the onion and garlic and cook, stirring, until golden, 6 to 8 minutes. Add the remaining ingredients, bring to a simmer, and continue to simmer, uncovered, stirring and scraping down the sides of the pan occasionally, 45 minutes. Cool, then puree in a blender until smooth.
• The barbecue sauce will keep, in a tightly sealed jar or container, in the refrigerator for several weeks.

Make the duck

• Arrange a rack in the center of the oven and heat the oven to 350°F.
• Pat the duck dry and season it all over with 1 tsp. salt and 1/2 tsp. pepper, total.
• Heat the oil in an oven-safe 12-inch skillet (2-inches deep) or braisier over medium heat until shimmering hot. Working in batches, if necessary, put the duck legs, skin side down, in the pan and cook, turning once, until the skin is a deep golden brown and the fat is rendered, about 10 minutes. Transfer, skin side up, to a plate.
• Drain all but 2 Tbs. fat from the pan (keep the excess for another use).  Add the onion and garlic to the pan and cook, stirring, over medium heat until golden, 6 to 8 minutes. Add the chicken broth, barbecue sauce, and chopped cilantro and bring to a simmer. Return the duck legs, skin side up, to the pan, nestling them in the sauce. Cover the pan tightly with a fitted lid or foil. Put in the oven and braise until the meat is tender, about 1-1/2 hours.
• Remove the lid and let the duck cool in the braising liquid, about 1 hour. When cool enough to handle, shred the meat, discarding the skin and bones. Strain the sauce through a sieve into a degreasing cup, pressing on, and then discarding the solids. In a 2- to 3-quart saucepan, combine the meat and just enough of the defatted sauce to coat the duck well (about 2 cups; strain and reserve the remainder for another use) and reheat. Swirl in the butter until incorporated and transfer to a serving dish. Garnish with the cilantro leaves and serve.