Preheat your oven to 375 degrees Fahrenheit
Saute the apples: Get out a large ovenproof saute pan and melt 2 tablespoons of the butter in it. Then toss in the apple wedges and saute them until they brown up, about 5 minutes. Take the apple slices out and reserve for later.
Brown up the chicken: Sprinkle some salt on the chicken and then dredge them in the ½ cup of flour. Add the remaining 2 tablespoons of butter to the hot pan and place the chicken in the pan skin side down. Let them brown up for 4 minutes, and then turn each piece of chicken over so that they can brown up for 4 minutes on the other side. After the chicken has browned up take them out of the pan and reserve for later.
Saute the onion and mushrooms: Add the onion and mushrooms to the pan and sautee them for 3 minutes. Then toss in the thyme and continue sauteing everything for another 2 minutes.
Deglaze the pan with the calvados and then add in the apple cider stirring until it comes to a low boil.
Place the chicken pieces back in the pan skin side up and then place it in the oven. Let everything bake uncovered for 30 to 40 minutes.
Finish the dish: Take the pan out of the oven and remove the chicken pieces setting them aside. Place the pan over high heat and toss in the reserved apple wedges. Stir everything together and let the sauce reduce by half. Once the sauce has reduced and thickened up, lower the heat to low and add in the heavy cream. Stir this all together and add salt & pepper to taste.
Serve the chicken on a plate with some of the onions, apples, and mushrooms. Pour some of the sauce over everything and enjoy immediately!