Turn your grill on and let it heat up to about 300 to 350 F degrees.
Season the zucchini, squash and mushrooms with salt and pepper.
Grill the vegetables, including the peppers on both sides until grill marks form. Remove from grill and set aside. Make sure you grill the peppers until they're charred.
Let the peppers cool then careful remove the skin and seeds from the peppers then wash them out.
Take a large tortilla and spread 2 tbsp of pesto over the top of the tortilla. Arrange grilled vegetables on half of the tortillas, some zucchini, squash, red onion, mushrooms and peppers. Top with about 1/2 cup of mozzarella cheese, use less if preferred. Flip over the other half of the tortilla to form half a circle and press down. You can use a panini press to grill the quesadilla or use a skillet. If you're using a skillet, spray the bottom of the skillet with cooking spray. Place the quesadilla and grill it on both sides until golden brown, about 3 minutes per side.
Repeat with remaining tortillas and grilled vegetables.
Cut each quesadilla in 4 and serve.
Store leftovers in an airtight container in the fridge for up to 3 days, be sure to reheat on the stove if you want to prevent the tortillas from getting soggy.
If you’d rather freeze the quesadillas be sure to wrap each quesadilla individually in parchment paper and freeze for up to 4 months.