4boneless, skinless chicken breast halves (about 1-3/4 lbs total)
Freshly ground nutmeg
Salt and freshly ground black pepper
4ouncesGruyère cheese, shredded
For the caramelized apples and onions:
1/2medium red onion, thinly sliced
2medium apples, peeled and cut into 1-inch chunks
2tablespoonsbrandy or apple cider
Preheat the oven to 350°F.
If the chicken breasts have the tenderloins attached, remove them and reserve for another use. Gently pound the breasts between 2 sheets of plastic wrap to a uniform thickness of 1/2-inch. Season with salt and pepper and a little ground nutmeg.
Place a portion of shredded cheese toward the center of each chicken breast and, starting from the narrower of the two ends, roll tightly and secure with a toothpick. Use your fingers to tuck in the open ends of the roll as best you can.
Beat the egg and milk together in a shallow dish. Combine the breadcrumbs with 1 teaspoon of salt, some freshly ground pepper and about 1/2 teaspoon of nutmeg, then spread them on a plate.
Carefully dip the chicken breasts in the egg-milk mixture, then roll them in the breadcrumbs, pressing gently to be sure the crumbs are adhering well.
Heat the vegetable oil in a large pan over medium heat. Add the chicken breasts and cook until the crumbs turn a light golden brown on all sides and the meat begins to firm, 4 to 5 minutes. Transfer to a baking dish and bake until the chicken is no longer pink in the middle, about 15 minutes. Remove from the oven and allow to rest for 5 minutes before slicing.
While the chicken bakes, make the caramelized apples and onions. Wipe out your pan, then melt the butter over medium heat. Add the sliced onions and season with salt and pepper. Cook, stirring occasionally, until the onions are golden brown, 5 to 6 minutes.
Add the apples, brandy, currant jelly and water. Continue cooking, stirring occasionally, until the apples are tender and golden,10 to 12 minutes longer. Taste and adjust the seasoning if necessary.
To serve, slice a few pieces from each chicken breast, plate individually and place the apples on the side.