Preheat oven to 400 degrees F. Line a baking sheet with parchment paper.
Heat olive oil in a large skillet over medium high heat. Add garlic, zucchini, bell pepper and corn; season with salt and pepper, to taste. Cook, stirring occasionally, until tender, about 3-4 minutes; set aside.
Spread pesto on tortilla; top with zucchini mixture and cheese, and then top with another tortilla. Repeat with remaining tortillas to make 4 quesadillas.
Place quesadillas onto the prepared baking sheet. Place into oven and bake until the cheese has melted, about 8-10 minutes.