How to Make It
Preheat the oven to 500°. In a large bowl, toss the onions with the melted butter. Season the ducks inside and out with salt and black pepper and rosemary sprigs in each cavity. Pack the onions into the cavity and set the ducks in a large roasting pan. Roast the ducks for 10 minutes. Lower the oven temperature to 300° and loosely cover the pan with the ducks for 4 1/2 hours, draining off the fat every hour.
Meanwhile, roast the red peppers over a gas flame, turning, until charred all over. Transfer to a paper bat and let steam for 10 minutes.
In a small saucepan of boiling water, blanch the carrots for 1 minute. Drain, transfer to a medium bowl and toss with 1 tablespoon of the butter.
Peel the peppers and discard the stems, seeds and ribs. Cut into 1/8-inch strips and add them to the carrots.
Discard the fat from the roasting pan. Add the orange juice, sherry and soy sauce and roast the ducks, uncovered, for 30 minutes. Transfer to a platter and let cool slightly.
Pour the pan sauce into a nonreactive saucepan, discarding any pieces of duck skin. Skim the fat and bring to a boil over moderately high heat. Boil until reduced to 1 1/2 cups, about 15 minutes. Strain and return it to the saucepan. (The recipe can be prepared to this point up to 4 hours ahead. Keep the ducks, sauce and vegetables covered separately at room temperature.)
Halve the ducks, discarding the onion and rosemary stuffing. Discard all the bones except the drumsticks, keeping the breasts attached to the legs. Rewarm the ducks in a low oven.
Melt the remaining 1 tablespoon butter in a small skillet. Add the oyster mushrooms and cook over moderately high heat, stirring occasionally, until golden brown, about 2 minutes. Season with salt and pepper.
Add the red bell pepper and carrot strips to the sauce and warm through over moderate heat. Season with salt and pepper.
Set the duck halves on 4 large warmed serving plates. Spoon the sauce over the duck, garnish with the mushrooms and chives and serve.