Preheat oven to 400 degrees. In a large skillet, heat 3 tablespoons oil over medium heat. Add onion and 1 teaspoon salt; cook, stirring occasionally, until onion is soft, about 5 minutes. Stir in garlic; cook 1 minute more.
Add zucchini and frozen corn kernels; cook, stirring occasionally, until zucchini is soft and corn is tender, about 6 minutes. Remove from heat; stir in cilantro, if using.
Brush one side of all tortillas with remaining tablespoon oil; lay 2 tortillas, oiled side down, on a baking sheet. Place half of the filling on each, and sprinkle with half the cheese. Place remaining 2 tortillas on top, oiled side up; press down gently with a spatula to seal.
Bake until cheese has melted and tortillas are golden brown, turning once, about 10 minutes. Remove from oven; let cool slightly. To serve, slice each quesadilla into wedges.
Shredded cooked chicken or sauteed shrimp are also delicious variations in quesadillas, as are roasted red peppers; peppers packed in oil have the best flavor.