Season the pork chops generously with salt and pepper. Heat 1 Tbsp. olive oil in a 12-inch skillet over high heat until lightly smoking. Add the pork chops and cook until first side is nicely browned, 4 to 6 minutes. Flip and continue to cook until the internal temperature registers 145 degrees F on an instant-read thermometer, about 3 minutes longer. Transfer to a plate and tent with foil. Do not wipe out skillet.
Lower heat to medium low and add the peaches, lemon zest, sugar, salt, and dried chili flakes. Stir gently until the peaches begin to soften but don’t lose their shape, 2 to 3 minutes.
Place the 2 pork chops on separate plates. Pour any juices from the plate back into the skillet and add butter and lemon juice. Cook, scraping up any browned bits from the bottom of the pan and swirling pan until butter is melted and incorporated into the sauce. Season to taste with salt and pepper. Stir in half of basil.
Divide the peaches between the two plates of pork chops and then pour the pan juices on top. Sprinkle with the remaining basil.