Cut the chicken into four or eight pieces and season with salt and freshly ground black pepper.
Heat half the butter and a little oil in a skillet and sauté the chicken in batches, skin-side-down, until lightly browned.
Pour off the excess fat, return all the chicken to the pan, add the Calvados or applejack and light with a match to flambé (keep the saucepan lid on one side in case of emergency).
Add the shallots and cook gently until softened but not brown.
Add the cider, cover and cook for 15 minutes, turning the chicken after 10 minutes.
Meanwhile, sauté the mushrooms in the remaining butter, covered, for 4 minutes.
Add the mushrooms and cooking juices, and the cream to the chicken and cook for 5 minutes. Remove the chicken and keep warm.
Continue cooking the sauce for 10 minutes, or until it is reduced enough to coat the back of a spoon. Adjust the seasoning to taste.
Return the chicken to the pan, bring to a boil, reduce the heat and simmer for 2 minutes to heat the chicken through.
Core the unpeeled apples and cut across into thin slices.
Fry in the clarified butter until golden brown on both sides.
Garnish the chicken with the apples and chopped parsley.