Let thawed pork chops come closer to room temp by setting out for 20-30 minutes before cooking. Salt and pepper both sides generously.
In a roomy heavy skillet, preferably cast iron, fully heated to medium high heat; drop in butter and garlic and spread evenly over the bottom of the skillet. Arrange pork chops evenly in one layer in pan, and let sear, undisturbed. Cook for 2 minutes on first side, flip and cook another 2 minutes on the other side. Do not disturb while they are searing, to get a nice, thick crust.
Remove chops from pan, set aside on a plate.
Deglaze pan with sherry, add balsamic vinegar, simmer and reduce by half. Add peaches, pork chops and basil and cook for another minute on each side, spooning sauce over peaches and chops as you go.
Immediately remove pork chops from skillet, to a resting plate, let rest 5 minutes. Remove sauce and peaches from heat while pork chops rest.
To serve, spoon peaches over pork chops, and spoon on extra sauce. Garnish with more fresh basil.