Combine beans and salsa in a small bowl; mash with a fork. Stir in zucchini. Layer 1 tortilla with half the bean mixture, sprinkle with 2 tablespoons cheese, and top with another tortilla. Repeat with remaining tortillas, bean mixture, and cheese. In broiler or toaster oven, cook quesadillas 1 minute on each side until cheese is melted and bubbly.