If using an electric burner, begin heating burner before seasoning pork chops. When cooking the first side of pork chops, use color as an indicator of when to flip them; use an instant-read thermometer to determine when cooked - do not rely on cooking times.
If using electric stove, turn burner to medium heat. Rub each side of pork chops with 1/8 teaspoon oil and sprinkle with salt and pepper. Sprinkle one side of each pork chop evenly with 1/8 teaspoon sugar, avoiding bone.
Place a 12-inch nonstick skillet on stove. Arrange pork chops, sugared-side down, with bone pointing toward center of pan. Use hands to press meat of each chop into pan. Cook until lightly browned, 4 to 9 minutes (chops should be sizzling after 2 minutes; (if not, raise the heat to medium-high to cook the pork chops uncovered, then reduce the heat to medium-low instead of low, cover the pork chops, and continue as directed). Using tongs, flip chops, positioning them in same manner. Cover skillet, reduce heat to low, and cook until center of each chop registers 140 degrees on instant read thermometer, 3 to 6 minutes. (Begin checking temperature after 2 minutes); chops will barely brown on second side. Transfer chops to platter, tent with foil, and let rest 5 minutes; pour liquid in skillet into small bowl.
While chops are resting, add 1/2 tablespoon butter to skillet over medium heat; add shallot and cook; stirring frequently, until softened, about 1 1/2 minutes. Add flour and dry mustard; cook, stirring constantly, 30 seconds. Slowly add broth, whisking constantly to avoid forming lumps. Add cider, reserved liquid from meat, and sage and bring to boil. Reduce heat to low and simmer 5 minutes. Remove pan from heat, whisk in whole-grain mustard and remaining 1/2 tablespoon butter; season with salt and pepper to taste. Spoon sauce over pork and serve immediately.