Broil corn and peppers on a foil-lined baking sheet coated with cooking spray 5 inches from heat about 5 minutes on each side or until peppers look blistered. Set corn aside.
Place peppers in a large zip-top freezer bag; seal and let stand 10 minutes to loosen skins. Peel peppers; remove and discard seeds. Cut into thin strips.
Stir together mayonnaise, lime juice, and cumin. Spread mixture evenly over 1 side of each tortilla half; top evenly with cheese, pepper strips, and corn. Fold tortillas in half.
Cook quesadillas, 1 at a time, in a large skillet coated with cooking spray over medium heat 30 seconds to 1 minute on each side or until lightly browned. Cut each quesadilla in half.
Note: Asadero or Oaxaca cheese may be substituted for Monterey Jack cheese.