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Preheat the oven to 375 degrees F (190 degrees C). Season pork with salt and black pepper.
Heat oil in an ovenproof skillet over high heat. Add pork; cook until browned on one side, 3 to 4 minutes. Flip pork; transfer skillet to the preheated oven. Cook until pork browned and still slightly pink in center, 20 to 25 minutes. An instant-read thermometer inserted into the center should read at least 145 degrees F (63 degrees C). Transfer pork to a plate.
Discard any excess oil from skillet. Place skillet over medium-high heat. Add chicken broth; bring to a boil, scraping any browned bits off bottom of skillet. Whisk in cream, horseradish, Dijon mustard, and cayenne pepper; continue cooking until reduced to a thick sauce, 3 to 4 minutes. Off heat, whisk in cold butter, then stir in chives.
Slice pork into ½-inch slices; top with sauce.