Step 1
Pat four 1½”-thick bone-in rib pork chops (about 2 lb. total) dry with paper towels. Sprinkle all over with 3 Tbsp. sugar, 1 Tbsp. Diamond Crystal or 1¾ tsp. Morton kosher salt, and 1 Tbsp. freshly ground pepper. Heat 2 Tbsp. vegetable oil in a large cast-iron skillet over high. Working in batches if needed, cook pork chops, turning halfway through, until deeply browned, about 5 minutes total. Transfer to a large plate.
Step 2
Working in batches if needed, cook 3 medium Granny Smith or Gala apples, halved through equators, and 3 medium shallots, peeled, halved lengthwise through root ends, cut sides down, in same skillet, gently pressing down on them with a spatula to create contact with pan, until golden brown on cut sides, about 2 minutes (it’s okay if shallots fall apart). Transfer apples to plate with chops.
Step 3
Reduce heat to medium, add 4 garlic cloves, finely grated, to pan, and cook, stirring constantly, just until fragrant, about 30 seconds. Add ¼ cup Dijon mustard, 3 Tbsp. all-purpose flour, and 2 Tbsp. unsalted butter; stir to coat shallots. Pour in 2 cups sweet hard apple cider, 1 cup low-sodium chicken broth, and 1 Tbsp. apple cider vinegar, scraping up browned bits and flour stuck to bottom of pan and incorporating into liquid. Add 10–12 sprigs thyme, tied together with kitchen twine, and bring mixture to a simmer. Partially cover (use a baking sheet if you don’t have a lid) and simmer until sauce is thick enough to coat a spoon, about 20 minutes. Taste and season with salt and pepper.
Step 4
Place pork chops and apples in sauce, arranging apples cut sides up, and partially cover. Simmer until an instant-read thermometer inserted into the thickest part of a pork chop registers 145°, 7–10 minutes. Remove from heat; sprinkle with finely chopped chives and season with more pepper to serve.