1. Preheat oven to 400°. Season chops with 1 tsp. salt and 1/2 tsp. pepper. Heat 2 tbsp. oil in a 12-in. heavy frying pan over high heat (a cast-iron pan ensures an especially good sear). Add chops and cook until golden brown on one side, about 4 minutes. Turn over, then put pan in oven to roast until pork is no longer pink in the center, about 8 minutes more.
2. Heat remaining 1 tbsp. oil in a medium frying pan over medium heat. Add shallot and cook until softened, about 4 minutes. Add raisins, vinegars, honey, and peaches and cook, stirring, until peaches begin to release their juices, about 5 minutes. Season to taste with salt and pepper.
3. Remove pork chops from oven. Add garlic, butter, and thyme to hot pan, basting pork with melting butter. Serve pork chops with pan juices and peaches.