Combine the ginger, 2 tablespoons vinegar and 1 tablespoon high-heat cooking oil, like canola, in a large resealable plastic bag. Sprinkle the pork with freshly ground black pepper and seal in the bag, squeezing out as much air as possible. Refrigerate at least 4 hours, or preferably overnight.
When ready to cook, move the pork to the counter to bring it to room temperature. Preheat the grill for cooking over medium heat (350 to 400 degrees F).
Cut the peaches in half crosswise around the pit (not through the stem) for easier release. Twist the halves in opposite directions to release the flesh from the pit. Twist the pit out of the peach, cutting tightly around the pit with a paring knife, if necessary. Drizzle the peaches cut-side up with the remaining 2 teaspoons vinegar.
Drain off the marinade and sprinkle the pork with 1/4 teaspoon salt. Rub the grill grates lightly with oil and grill the pork until it has nice grill marks and releases easily from the grill, about 8 minutes.
Turn the pork and cook another 5 minutes. Once more, turn to another side and cook an additional 5 minutes. Remove the pork and cover it loosely with foil. Allow to rest 5 to 10 minutes to let the juices redistribute.
Meanwhile, place the peaches on the grill cut-sides down and cook until they have nice grill marks, release easily from the grill and are softened, 8 to 10 minutes.
Sprinkle the pork and peaches with basil and additional salt and pepper to taste. Slice and serve.
If one end of the pork tapers off thinly, fold an inch or two under itself and hold it in place by tying with butcher string, to ensure more even cooking. Nutritional analysis includes using enhanced pork tenderloin, commonly sold at mainstream grocery stores. Natural pork tenderloin contains less sodium.