Place the cheeses, the chopped basil and parsley and the crushed garlic into a large mixing bowl.(I think these would be really good with mozzarella, but I was all out.)
Quarter the cherry tomatoes and toss into the mixing bowl with the cheese. Mix her up.
Meanwhile…fire up the grill and grill the red pepper slices and the squash slices. Then dice.
Toss the diced grilled squash and diced grilled red pepper in with the cheese mixture.
Spoon the mixture into the the tortillas. Fold over, or cover 1 tortilla with the mixture and top with another tortilla. However you like…in the end, it won’t matter how you use the mixture in the tortilla. It’s really about the ooey-gooey goodness that will result from grilling the quesadilla.
Place the tortillas on the grill for a few minutes on each side, or until the cheese is oozing out the sides of the tortillas…as sure sign they are ready for consumption.
Let cool and cut grilled quesadillas into little triangles.
Serve Summer Squash Quesadillas as an appetizer or main meal.