Season the pork chops with salt and freshly ground black pepper. Add the oil to the sauté pan and brown the pork chops on both sides, cooking for about 4 minutes per side, depending on the thickness. When the pork chops have reached an internal temperature of 155°F, remove them from the pan and set them aside to rest, loosely tented with foil.
Add the shallot and thyme to the same pan and cook for a minute or 2. Add the peaches and sauté until lightly browned. Add the white wine and bring to a simmer. Simmer for just a minute or 2 and then remove the pan from the heat. Swirl in the honey and the butter and season to taste with salt and freshly ground black pepper.
Pour the sauce over the pork chops and serve with shredded fresh basil on top.
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