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Step 1
Pat the pork chops dry and season generously with salt and pepper. Sprinkle with thyme on both sides. Let sit at room temperature for least 15 minutes or for up to an hour.
Step 2
Heat the ghee or olive oil in a cast iron skillet over medium-high heat. Once hot, arrange the pork chops in a single layer. Sear the pork chops until they’re golden brown on the bottom, about 5-7 minutes. Turn and cook on the other side until golden brown, about 5 minutes longer. Keep cooking, flipping and turning the chops as needed, until an instant-read thermometer inserted in the thickest part reads 140˚F (60˚C)—the cooking time will depend on the thickness of the chops. Transfer the chops to a plate and tent lightly with foil to keep warm (the temperature will climb to 145˚F as it rests).
Step 3
Pour off most of the fat in the skillet. Put the skillet over medium heat and add the shallots and garlic. Cook, stirring, until fragrant and softened, 2-3 minutes. Stir in the capers and cook 30 seconds. Pour in the white wine and simmer until reduced by half (there won’t be much liquid left). Remove the pan from heat and stir in the butter and parsley. If any juices have accumulated under the pork, pour them into the sauce as well. Taste the sauce and season with salt and pepper as needed. Spoon the sauce over the pork chops and serve.