Quarter sweet peppers lengthwise; remove seeds and membranes. Brush outsides of pepper quarters lightly with oil. Spread insides with pesto; top with cheese.
For a charcoal grill, grill sweet pepper quarters, filled sides up, on the rack of an uncovered grill directly over medium coals for 5 to 7 minutes or until bottoms are lightly charred and cheese is softened. (For a gas grill, preheat grill. Reduce heat to medium. Place sweet pepper quarters on grill rack over heat. Cover and grill as directed.)