Grilling heightens the sweetness and flavor of the nectarines. Because they have such thin skins, nectarines don't require peeling for this dish. However, you may substitute fresh peeled peaches if you prefer.
Cut pork horizontally through center of meat, cutting to, but not through, other side using a sharp knife; open flat as you would a book. Place pork and nectarine halves, cut sides down, on grill rack coated with cooking spray. Grill pork 5 minutes on each side or until a thermometer registers 160°. Grill nectarine halves 4 to 5 minutes on each side or until thoroughly heated. Remove pork and nectarine halves from grill. Let pork rest 10 minutes.
Cut nectarine halves into slices. Thinly slice pork. Combine spinach and vinaigrette in a large bowl; toss gently to coat.
Divide spinach mixture evenly on each of 6 plates. Top each serving evenly with nectarine slices and pork slices. Sprinkle with cheese. Sprinkle evenly with pepper, if desired.