Preheat the oven to 450 degrees F.
Remove the neck and giblets
from the cavity of the ducks and reserve. Cut the wings off the ducks and reserve. Rinse the ducks under cold running water and pat dry with paper towels. Using the tip of a sharp paring knife, prick the ducks all over, inserting knife at an angle to pierce just the skin, not the flesh.
Season the ducks well with salt and pepper. Place them on a rack in a shallow roasting pan and roast
until browned and crisp
, 1 1/4 hours. Remove the roasting pan at 30 minute intervals, drain
off the fat, and again prick the skin.
While the ducks are roasting, rinse the neck, giblets, and wings and pat dry. Cut the wings and the neck into several pieces. Heat the oil in a large saucepan
over medium-high heat. Add the neck, giblets, and wings. Cook, stirring often, until golden brown, 8 to 10 minutes. Reduce the heat to medium and add the onion, carrot
, and garlic. Cook until the vegetables are lightly browned and softened, 5 to 8 minutes. Increase the heat to medium-high and pour in the wine
. Bring to a boil, stirring to pick up any browned bits on the bottom. Boil until almost all of the liquid has evaporated. Add the celery
, thyme, black peppercorns
, bay leaf
, tomato paste, and stock. Reduce the heat to medium and simmer, skimming off any scum that rises to the surface, until the ducks are ready to come out of the oven.
When the ducks are done, transfer to a carving board, cover loosely with foil, and let rest for 15 to 20 minutes.
While the ducks are resting, strain
the stock and discard the solids. Measure the liquid. If there is less than 2 cups, add water to measure this amount and pour into a small saucepan. If there is more than 2 cups, return to the saucepan and boil until reduced to this amount.
Bring the liquid back to a simmer
over medium-high heat. Combine the flour and butter in a small heatproof bowl and use a fork to work it into a smooth paste. Add a little of the stock to the paste and whisk
until smooth. Pour the flour mixture into the saucepan and simmer, whisking, until slightly thickened, 2 to 3 minutes. Stir in the green peppercorns. Remove the saucepan from the heat, stir in the mustard, and season the sauce with salt and pepper. Cut the ducks into serving pieces. Spoon a small amount of the sauce over the duck
and serve warm with any remaining sauce on the side.