Preheat oven to 400°F.
Season pork chops with salt and pepper. Heat oil in 10" ovensafe skillet over medium-high heat until shimmering. Add chops and cook until browned on both sides, 3-4 minutes per side. Transfer chops to a plate and set aside. Pour off and discard any grease in pan.
Lower heat to medium. Add butter to skillet. When melted, add peach slices. If they are less-than-ripe, add sugar to taste. Cook, stirring often, until peaches are soft, 1-3 minutes.
Remove skillet from heat. Add bourbon and swirl pan. Light a long-handled match and pass over skillet carefully until bourbon ignites. When flames subside, return to heat and use a wooden spoon to scrape up any browned bits (fond) from the bottom of the pan. Season sauce with salt, pepper and/or sugar, to taste.
Return chops to skillet and lay 4 basil leaves on each chop. Place peach slices on top of basil. Place skillet in oven until chops are done, about 4 minutes for medium. Divide chops and peaches between two plates and spoon pan sauce over each serving.