Preheat barbecue on LOW. Combine salsa, onions and jalapeño pepper in a small bowl. Lightly brush one side of each flour tortilla with olive oil. (This will be the outside of the quesadilla.) Spread two of the tortillas with the salsa mixture, then sprinkle with grated cheese. Cover with remaining tortillas.
Place the quesadillas directly on the cooking grids, and grill about 3 minutes per side, checking the bottom frequently.
Transfer to a wooden cutting board and let sit for 1 minute before slicing with a sharp knife or pizza wheel.

MAKE IT EASIER WITH THESE GRILL ACCESSORIES.