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Preheat oven to 375 degrees F.
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Place a 10-12 inch cast iron skillet over medium-high heat. When hot add 1 tablespoon of olive oil and heat until lightly smoking.
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Season pork chops well with salt and pepper and add them to the skillet.
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Cook on one side until nicely browned, for about 4 to 6 minutes.
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Flip and continue to cook for another 3-4 minutes. Transfer to a plate and tent with foil.
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Lower heat to medium low and add butter to the skillet.
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Add the peaches, lemon zest, brown sugar, lemon juice, and red pepper flakes. Stir gently and cook for about 1-2 minutes.
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Add the pork chops back to the skillet and transfer to the preheated oven.
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Bake for 10 minutes or until the internal temperature of the pork chops registers 145°F on an instant read thermometer.
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Remove from oven, gently stir the peaches so they are covered in the caramelized sauce. Divide the peaches between two plates, add the pork chops to the place and then pour the pan juices on top.
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Serve immediately.