Heat oil and butter in a heavy skillet over medium-high heat. Cook pork chops in the hot oil mixture until browned on both sides and pork is slightly pink in the center, 5 to 7 minutes per side. An instant-read thermometer inserted into the center should read at least 145 degrees F (63 degrees C). Remove pan from the heat; transfer pork chops to a plate.
Stir garlic into the pan and place over medium-high heat; cook and stir for 30 seconds. Pour in vinegar and scrape up any browned bits from the bottom of the pan. Add apple cider and Dijon mustard, bring mixture to a boil, and cook until sauce is reduced and thick, 3 to 4 minutes. Stir in rosemary and red pepper flakes; season with salt and black pepper to taste.
Return pork chops to the pan to warm slightly, 1 to 2 minutes per side.