Season the duck breasts with salt and pepper.
In a large, heavy-bottomed skillet, heat the butter over high heat until it foams and subsides. Add the seasoned duck breasts and cook for 1 minute on each side. After 1 minute of cooking on the second side, add the apples and cook for an additional 4 minutes.
Add the vinegar and swirl the pan to mix the vinegar with the duck fat and butter. Add the peppercorns and cook for another 2 minutes, adding more vinegar, if necessary, to keep the pan from getting to dry.
Slice the breasts on a severe bias and serve with Potato Goulash.
In a large, heavy-bottomed skillet, heat the olive oil over medium heat until hot but not smoking. Add the onions and reduce the heat to low. Cook the onions over low heat for 30 minutes, so that the onions are very soft and caramelized.
Add the potatoes and most of the paprika. Stir well to combine and season well with salt and pepper. Add enough water to the pot to just cover the potatoes and stir in the tomato paste. Simmer for 15 to 20 minutes, until the liquid has reduced by half. Stir in the remaining paprika and serve immediately.
Recipe copyright 2001, Mario Batali. All Rights Reserved.