Step 1

Preheat oven to 400°F. Heat oil in a large cast-iron skillet over medium-high. Pat pork chops dry. Sprinkle both sides evenly with salt and pepper. Add pork to skillet. Cook, undisturbed, until bottoms are golden brown, 5 to 6 minutes (pork will not be cooked through). Transfer pork to a plate; set aside.

Step 2

Reduce heat under skillet to medium. Add butter to skillet; scrape up brown bits stuck to bottom of skillet using a wooden spoon. Add shallot, garlic, flour, and rosemary. Cook, stirring constantly, until fragrant, about 30 seconds. Stir in stock and mustard. Bring to a simmer over medium. Simmer, undisturbed, until slightly reduced, about 3 minutes.

Step 3

Return pork, browned side up, and any juices to mixture in skillet. Transfer skillet to preheated oven; roast until a thermometer inserted into thickest portion of chops registers 145°F, 6 to 8 minutes. Remove skillet from oven. Transfer pork to serving plates.

Step 4

Return skillet to stovetop; bring mixture to a simmer over medium. Simmer, undisturbed, 2 minutes. Whisk in buttermilk; return to a simmer over medium. Simmer, whisking often, until buttermilk sauce is slightly thickened, 1 to 2 minutes. Serve pork alongside hot cooked egg noodles and buttermilk sauce; garnish with additional rosemary.