Step 1

Pat pork chops dry with a paper towel. Combine salt and sugar in a small bowl. Season pork chops generously on all sides with salt/sugar mixture (you may have some seasoning mixture left over; reserve for another use or discard). Transfer to a wire rack set in a rimmed baking sheet. If dry-brining chops overnight, refrigerate, uncovered, at least 8 hours and up to 24; otherwise proceed immediately to Step 2.

Step 2

When ready to cook chops, preheat oven to 250°F. Season chops with pepper. Place baking sheet with pork chops in oven and cook until an instant-read thermometer inserted into the center of the chops registers 100 to 110°F for medium-rare, about 30 minutes, or 110 to 120°F for medium, about 35 minutes. To prevent overcooking, start checking temperature 5 to 10 minutes before suggested time. Remove from oven.

Step 3

Heat oil in a large stainless steel or cast iron skillet over high heat until smoking. Place pork chops in skillet and cook, turning occasionally, until browned and an instant-read thermometer registers 120 to 130°F for medium-rare or 130 to 140°F for medium, about 3 minutes. Stack pork chops with tongs, hold them on their sides, and sear the fat caps on the edges until crisp, about 1 minute. Remove pan from heat, transfer chops to a clean rack set in a rimmed baking sheet, and let rest for 3 to 5 minutes.

Step 4

Pour fat from skillet. Add 1 tablespoon butter and melt over medium-high heat. Add shallot and thyme and cook, stirring, until softened, about 2 minutes. Stir apple cider and bring to a simmer. Lower heat to medium and simmer until liquid is slightly reduced, about 4 minutes. Whisk in cider vinegar and remaining 3 tablespoons butter. Remove from heat, season with salt and stir in parsley. Serve chops, spooning sauce on top.