Pull the leaves from the sprig of rosemary. Combine them with the garlic and oil in a shallow bowl.

Pat the duck breasts dry with kitchen paper. Brush them with the marinade and allow to stand for at least 2 hours before cooking.

Preheat the oven to 180C. Cut a cross in the flat side of each chestnut with a sharp knife.

Place the chestnuts on a baking sheet with the oil and shake the sheet until they are coated with oil. Bake for 20 minutes, then peel.

Place the peeled chestnuts in a heavy saucepan with the milk, onion, carrot and bay leaf. Cook slowly for about 10-15 minutes until the chestnuts are tender, then season. Discard the bay leaf. Press the mixture through a sieve.

Return the sauce to the pan. Heat gently while the duck breasts are cooking, Just before serving, stir in the cream. If  the sauce is too thick, add a little more cream. Preheat the frill, or prepare a barbeque.

Grill the duck breasts until medium-rare, for about 6-8 minutes. They should be pink inside. Slice into rounds and arrange on warmed plates. Serve with the heated sauce.