3/4 cup grated Monterey jack cheese (about 3 ounces)
1/4 cup packed fresh coriander sprigs, washed, dried and chopped coarse
Cut onion crosswise into 1/4-inch-thick slices and arrange slices on a tray, keeping them intact. Brush both sides of slices lightly with oil and season with salt and pepper. Grill onion on a lightly oiled rack set 5 to 6 inches over glowing coals 4 minutes on each side, or until lightly charred and softened. Transfer onion as grilled to a bowl, separating rings. Brush 2 tortillas lightly with oil on one side and put, oiled side down, on a platter. Divide onion, Monterey jack, and coriander between tortillas and cover with remaining 2 tortillas. Brush tops of quesadillas lightly with oil.
With a metal spatula transfer quesadillas to a rack set 5 to 6 inches over glowing coals and grill until undersides are golden brown, about 1 minute. Sandwiching each quesadillas between 2 metal spatulas, flip quesadillas over and grill until undersides are golden brown, about 1 minute. Transfer quesadillas to a cutting board and cut into wedges.
Serves 2 as a light luncheon main course or side dish.