Heat a large skillet over medium high heat. Add a generous amount of salt and pepper to both sides of the pork chops. Add the olive oil to the skillet, when the oil shimmers, add the pork and sear on both sides for about 3-4 minutes. Reduce the heat to medium and continue cooking for about 8 minutes, or until the pork chops are cooked through.
In a small bowl, whisk together the balsamic vinegar and honey. During the last few minutes of cooking, pour the balsamic sauce over the pork chops. Remove the skillet from the heat and add the sliced peaches into the skillet.
Preheat the oven broiler to high and transfer the skillet to the oven on the middle rack and broil for 4-5 minutes or until the peaches are lightly charred.
Remove skillet from the oven and plate with quartered cheese, fresh basil, and chili flakes.
Serve the pork with the peaches and balsamic sauce from the pan and add thin sliced ribbons of basil for extra flavor.