Slit the buns horizontally. Brush the cut sides with olive oil. Tear off a 24-inch piece of heavy foil. Fold in half to make a double thickness that measures 12x12 inches. Coat foil lightly with nonstick cooking spray.
Place the bottom halves of buns in center of foil. Top with mozzarella, tomato, and artichokes. Sprinkle with olives, Parmesan, basil, and pepper. Replace tops of buns. Bring up the two opposite edges of foil and seal with a double fold. Fold in the remaining ends to completely enclose bread.
Grill packages on rack of uncovered grill directly over medium coals 15 minutes or until heated, turning once.
To serve, cut each bun in half crosswise. Makes 4 servings.