Divide chicken into 8 – 10 segments. Season the chicken pieces with salt and pepper then lightly flour. Heat oil in a heavy based casserole. Place the chicken pieces in the oil and cook for 3-4 minutes on each side or until golden brown. Remove chicken from the casserole and add the onion, carrot and cook until the onions are translucent. Put the chicken back in the casserole and add the calvados. Ignite and then allow the flames to subside before deglazing with the apple cider. Add the bouquet. Use a wooden spoon to scrape the bottom of the pot and bring to the boil, then add the stock. Cook on a gentle heat for 40 minutes.
Meanwhile heat a large non-stick pan over a medium heat and add the mushrooms and apples. Sauté for 6-8 minutes or until they are lightly brown.
Remove the chicken pieces from the sauce and put into a warm platter along with the carrots and apple and mushroom mixture. Strain the sauce into a clean saucepan and bring to the boil. Add the cream and a squeeze of lemon juice and simmer until the sauce thickens slightly. Pour over the chicken.
I like to serve this simply with steamed waxy potatoes.