How to Make It
In a small dry skillet, toast the star anise and caraway seeds until fragrant, about 2 minutes. Transfer the spices to a spice grinder and let cool completely, then grind to a powder. In a pot large enough to hold both ducks in a single layer, whisk the spices into the orange juice.
Prick the ducks all over with a sharp fork and loosen the skin with your fingers. Place the ducks in the pot and massage them with the marinade. Cover and marinate in the refrigerator for 8 hours.
Remove the ducks from the marinade and pat dry inside and out; discard the marinade. Set the ducks on a rack set over a roasting pan and refrigerate uncovered for 24 hours. Remove the ducks from the refrigerator 2 hours before roasting.
Preheat the oven to 325°. Roast the ducks for about 2 1/2 hours, until the skin is deeply golden and crisp: Every 45 minutes, tilt the ducks over a bowl to drain the liquid from the cavities, then replace them on the rack. Prick the skin to release the fat and baste the ducks with the fat in the pan.
In a medium saucepan, combine the sugar and lemon juice. Bring to a simmer over moderate heat and cook until lightly caramelized. Stir in the stock, orange juice, Grand Marnier, shallot, orange zest, cloves and cinnamon (it will bubble a lot). Simmer over moderate heat until the sauce is thickened, about 30 minutes. Season with sherry vinegar and sea salt. Strain the sauce through a fine sieve and serve with the duck.