Put the oil and butter into a frying pan or flame proof casserole and heat gently over a low heat.
Peel and finely chop the shallots. Add them to the oil and butter in the pan or casserole, increase the heat to moderate, and fry, stirring occasionally, for 3–4 minutes, or until they are soft.
While the shallots are cooking, rinse, dry, quarter, core, and slice the dessert apples, then add them to the shallots and sprinkle them with the brown sugar. Raise the heat to fairly high and fry until the mixture starts to turn a golden caramel color.
Lift the shallots and apple slices from the frying pan or casserole with a slotted spoon and set aside.
Add a little more oil to the pan, if necessary. Add the chicken breasts and fry them over a fairly high heat for about 6 minutes, turning once, until golden.
Pour the cider over the chicken. Bring it to the boil and simmer, uncovered, for about 8–10 minutes, stirring occasionally and turning the chicken once more, until it is cooked. The chicken is ready if the juices run clear when it is pierced with the tip of a knife.
When the chicken is ready, stir in the Worcestershire sauce and whipping cream, and season to taste with salt and black pepper. Return the shallots and apple slices to the pan and warm them through for another 1–2 minutes, but do not allow the sauce to boil.
Serving Suggestion: Serve the chicken with microwaved jacket potatoes (see below), or with rice or buttered noodles and a green salad or vegetables.
Variation: The sauce can be made with a dry white wine or richly ﬂavored chicken stock instead of cider, if you prefer, but you must use dessert apples as cooking apples would lose their shape.
Cook's Tip: Microwaved jacket potatoes can make a speedy accompaniment to many main course dishes. Prick the skins of two evenly sized potatoes. Place on a piece of kitchen paper in the microwave and cook on high for 6–8 minutes, turning them over halfway through. Wrap in foil and leave to stand for 3–4 minutes.