How to Make It
Season the duck with salt and pepper. In a large cast-iron casserole, heat 1 tablespoon of the olive oil. Add the duck to the casserole skin side down and cook over moderate heat until browned and the fat is rendered, about 7 minutes. Flip the duck and cook until browned all over, 5 to 8 minutes longer. Transfer to a plate.
Pour off all but 2 tablespoons of fat from the casserole. Add the carrots, fennel, leek and shallots and cook over moderate heat, stirring occasionally, until just starting to soften, about 5 minutes. Add the apple cider, thyme, bay leaves and tarragon and bring to a boil. Return the duck to the casserole, cover and braise over moderately low heat until the duck is tender, about 1 hour and 15 minutes.
Meanwhile, in a large skillet, cook the pancetta in 1 tablespoon of the olive oil over moderate heat, stirring occasionally, until browned and just crisp, about 5 minutes. Using a slotted spoon, transfer the pancetta to a plate. Add the onions and a generous pinch of salt to the skillet and cook over moderate heat, stirring occasionally, until browned in spots and heated through, about 3 minutes; transfer to the plate. Add the remaining 2 tablespoons of olive oil to the skillet, then add the mushrooms and a generous pinch of salt and cook over moderately high heat, stirring occasionally, until browned and tender, about 7 minutes. Transfer to the plate and keep warm.
Transfer the duck to a plate and keep warm. Using a slotted spoon, transfer the vegetables to a medium bowl. Skim off the fat from the casserole, then return the vegetables to the casserole and bring to a boil. Simmer over high heat until reduced by half and the vegetables are coated in the sauce. Stir in the vinegar and honey and season with salt and pepper.
Transfer the vegetables and sauce to a platter and arrange the duck legs on top. Scatter the pancetta, onions and mushrooms on top and serve.