Step 1: Prepare the duck: Remove the packet of giblets from the body cavity of the duck and set aside for another use. Remove and discard the fat just inside the body and neck cavities. Trim off any excess neck skin. Rinse the duck, inside and out, under cold running water, then drain and blot dry, inside and out, with paper towels.

Step 2: Turn the duck on its back, and with a sharp knife or kitchen shears, cut from the neck to the main cavity on either side of the backbone and remove it. Cut through the breastbone and remove the cartilage to separate the duck into two halves.
Cut off and discard the outer 2 tips of each wing.

Lightly score the duck skin, particularly the portion covering the breast.

Using a very sharp knife, make cuts in a crosshatch pattern about 1/2 inch apart.

(The idea is to cut through the skin but not the meat. This will help the fat cook out.)

Step 3: Place the duck halves in a large cast iron skillet or roasting pan and season generously on all sides with salt and pepper. Sprinkle the chopped garlic, sliced shallots, and chopped rosemary all over the duck halves. 4. Drizzle the oil all over the duck, patting it and the garlic, shallots, and rosemary onto the meat with your fingers. Let the duck marinate, covered, in the refrigerator for 2 to 4 hours.

Step 4: Preheat your wood-burning oven according to the manufacturer’s instructions to medium-high (400 degrees F). Arrange the whole shallots and 4 sprigs of rosemary on top of the duck and place in the oven.

Step 5: Place the pan with the duck in the wood-burning oven. Cook until the skin is browned and crisp and the meat is cooked through and tender, 1 to 1-1/4 hours for well-done duck with crisp skin (if you prefer your duck medium, it will take about 45 minutes). To test for doneness, use an instant-read meat thermometer: Insert it into the thickest part of a thigh, but not so that it touches bone. The internal temperature should be about 170 to 180 degrees F. Remove the duck halves from the skillet or roasting pan and keep warm.

Step 6: Transfer the hot pan to the stovetop or the side burner of a grill. (If the pan has lost heat, rewarm it over a medium flame.) Deglaze the pan with the red wine vinegar and chicken stock; bring to a boil. Boil until the liquid is reduced by half. Lower the heat to maintain a simmer. Whisk in the butter a few pieces at a time to thicken the sauce. Season with salt and pepper.

Step 7: Spoon the sauce over the duck and serve immediately, garnished with the roasted shallots and 3 sprigs of fresh rosemary.