Preheat oven to 450°F.

Pat pork chops dry and season both sides well with salt and pepper. Heat 1 tablespoon butter in a heavy skillet over moderately high heat, add 2 chops and brown for 2–3 minutes on each side. Lift out and move to a large shallow baking pan. Repeat with 1 more tablespoon butter and the other 2 chops.

Melt 1 tablespoon butter in skillet, add shallots and cook over moderate heat, turning occasionally, until golden brown and tender, about 10–15 minutes. Add cider and boil, stirring and scraping up brown bits, 3–5 minutes, or until liquid reduces by about a half. Turn off heat and swirl in 1 last tablespoon of butter.

Spoon shallots and sauce around chops and roast in lower third of oven until thermometer inserted horizontally into center of 1 chop (do not touch bone) registers 150°, about 7 minutes. Allow chops to rest, loosely covered with foil, 5 minutes (temperature will rise to 155° while resting). Plate chops with shallots and sauce; serve with roasted root vegetables, cabbage or squash; pour the same cider for dinner that was used for the cooking.