To make compote, place apples, juice, honey, vinegar and a bit of salt and pepper in a large saucepan and bring to a boil. Lower heat and simmer for about 30 minutes, uncovered, stirring once in a while to avoid burning.

When apple pieces are soft, remove compote from heat. Cool down and store covered in refrigerator for up to three days or use when still warm and duck is ready. Taste for seasoning before using and adjust, if needed.

Heat a grill, grill pan or a 12-inch heavy skillet over high heat until very hot.

While pan is heating, pat duck breasts dry and score skin at one-inch intervals with a sharp knife (do not cut into meat), then sprinkle all over with salt and pepper.

Put breasts, skin sides down, in skillet and reduce heat to moderate. Cook for about five minutes, until skin is crispy and brown. Fat will be rendered and you can save it for another use.

Turn breasts, insert a meat thermometer into center of one of the breasts, and cook until it registers 130 degrees Fahrenheit (see note) six to 10 minutes.

Transfer to a cutting board and let rest 5 minutes. Then, holding a sharp knife at a 45-degree angle, cut each duck breast into thin slices and serve with warm compote.