Heat 1 tablespoon olive oil in 12-inch nonstick skillet over medium-high heat and cook onion, pepper and zucchini, stirring occasionally, 4 minutes or until tender.
Reduce heat to medium and stir in 1-1/2 cups sauce. Simmer, stirring occasionally, 5 minutes or until sauce is thickened.
Evenly spread sauce mixture on tortillas, leaving a 1-inch border. Sprinkle evenly with cheese and fold in half; set aside. Clean skillet.
Heat remaining 1 tablespoon olive oil in same skillet over medium heat and cook quesadillas, two at a time, turning once, 4 minutes or until golden brown and cheese is melted.
Cut quesadillas into wedges and serve with remaining sauce, heated.