Very sharp Seville oranges are best in this classic dish, named after the mistress of Charles II. They are available only in January and February, so if you are using sweet oranges, add a squeeze of lemon juice to ensure a tangy flavour.
Heat the oven to 200°C (400°F, gas mark 6). Remove any excess fat from the openings of the duck. Rub the cayenne pepper, cloves, salt and pepper into the skin. Cut one orange into wedges and tuck the wedges inside the cavity.
Place the duck on a rack in a roasting tin and roast in the oven for 30 minutes. Prick the skin all over with a fork, then reduce to 180°C (350°F, gas mark 4) and roast for a further 1¼-1½ hours, or until cooked but with the juices running slightly pink when the thickest part is pierced. Pour off the excess fat once or twice during cooking.
Remove the zest from the remaining oranges, then squeeze the juice into a bowl. Remove the duck on its rack from the tin, cover with foil and set aside to rest. Skim the fat from the juices and add the sherry to deglaze the tin, stirring over a moderate heat.
Blend the cornflour to a paste with a little of the orange juice, then stir in the remaining juice. Add to the tin, stirring until boiling, thickened and clear. Stir in the orange zest, chopped mint and honey and boil for 1 minute. Add salt and pepper to taste.
To serve, cut the duck into quarters with a heavy knife or poultry shears, pour over the orange sauce and garnish with orange wedges and mint sprigs. Serve with fresh minted peas and boiled potatoes.