Position a rack in the center of the oven and heat the oven to 350ºF.
Season the chicken pieces generously with salt and pepper. In a straight-sided 10- or 11-inch ovenproof sauté pan with a lid, heat the oil over mediumhigh heat until very hot. Arrange the chicken pieces skin side down in the pan (it’ll be crowded), cover with a splatter screen, if you have one, and cook until deeply browned, about 5 minutes. Turn the pieces over and cook until the other sides are deeply browned, 3 to 5 minutes more. Transfer to a plate. Pour out and discard all but 1 Tbs. of the fat from the pan. Set the pan aside to cool for a few minutes.
Return the pan to medium-high heat, add the apple pieces, and cook, turning once, until both cut sides are golden brown, about 2 minutes per side. Transfer to a different plate. Carefully pour the cider into the pan and bring to a boil, scraping the browned bits from the bottom of the pan with a wooden spoon.
Whisk the mustard into the cider. Return the chicken to the pan, along with any accumulated juices. Add the marjoram sprigs and cover. Transfer the pan to the oven and braise for 10 minutes. Add the apples and continue to braise until the chicken is fork-tender and the drumstick meat starts to come away from the bone, 35 to 40 minutes more.
With a slotted spoon, transfer the chicken and apples to a large serving dish and keep warm by covering the dish loosely with foil. Discard the marjoram sprigs. Tilt the sauté pan and skim off as much fat as possible from the sauce. Bring the sauce to a boil over medium-high heat and whisk in the cream. Reduce the heat to medium-low and simmer until the sauce is slightly thickened, about 5 minutes. Season to taste with salt and pepper. Pour the sauce over the chicken, sprinkle with the chopped marjoram, and serve.
Serve over noodles.
Try a dry, fruity Riesling from Alsace, such as the Domaine Albert Boxler.