Season pork chops generously with salt and pepper on all sides, and then set aside.
In a small mixing bowl, combine walnut oil, honey and vanilla. Mix until well combined, and then set aside.
In a large skillet over medium heat, melt the butter. Add peach slices and rosemary. Then add about 1/4 of the oil/honey mixture and move peaches around to gently coat. Cook peaches until lightly browned on both sides, about 2 minutes. Transfer peaches to a small dish. Cover.
In the same skillet (no need to clean it out), cook pork chops on both sides until golden brown. As you cook them, add most of the remaining oil/honey mixture, and allow it to thicken in the pan/coat the chops as they cook.
Once pork chops are almost done cooking, add peaches back to the pan, along with the walnuts and thyme. Move nuts and peaches around to coat. Cover and cook for an additional 3-4 minutes.
Pour any remaining oil/honey mixture on top and serve immediately.