Turn your grill on to a high heat.
Pat pork chops dry with a paper towel.
Rub each side of the pork chops with a basil leaf.
Brush with 2 Tablespoons of the olive oil.
Generously sprinkle with salt and pepper.
Grill the chops until you see grill marks, about 4 to 5 minutes on each side. Use an instant-read thermometer to ensure that the internal temperature is 145º F, for medium rare; or 150º for medium.
Remove to a plate, tent loosely with foil and let rest while you grill the nectarines.
Brush each of the cut sides of the nectarines with olive oil and place each, cut side down, onto the grill.
Grill for about 2 to 3 minutes or until golden brown.
To continue to soften the nectarines, turn them over and grill for 1 to 2 minutes.
Remove the nectarines from the grill and immediately top each with blue cheese.
Drizzle with honey and sprinkle with sliced basil leaves, pine nuts, and black pepper.
Serve with the pork chops.