Grill the veggies on indoor or outdoor grill until charred and tender. Set aside.
Put some grilled veggies on the lower half of tortilla and top itwith grated cheese. Fold the top half onto the cheese and press lightly.
Grease the grill and cook the quesadilla until grill marks form and the cheese is melted, about 2-3 minutes per side.
Repeat with the remaining tortillas and veggies.