Boneless Pork Chop with Shallot Mustard Sauce

Preheat oven to 350 degrees F (175 degrees C). Season pork chops with salt, pepper, and Italian seasoning. Heat butter and olive oil together in a skillet over medium-high heat until butter begins to foam; cook pork chops in the hot butter-oil mixture until golden brown, about 3 minutes per side. Transfer pork chops to a baking dish, keeping the pan juices in skillet. Bake pork chops in the preheated oven until no longer pink in the center, 10 to 15 minutes. An instant-read thermometer inserted into the center should read at least 145 degrees F (63 degrees C). Cook and stir onion and shallots in the skillet with pan juices over medium heat until softened, 3 to 5 minutes. Pour chicken stock and cooking wine into onion mixture, and bring to a boil while scraping the browned bits of food off of the bottom of the pan with a wooden spoon. Whisk half-and-half, horseradish mustard, lemon juice, and thyme into onion mixture until mustard sauce is smooth and heated through, about 5 minutes. Serve pork chops drizzled with mustard sauce.