Preheat oven to 450 degrees F. Coat sides and bottom of 13x9x2-inch baking pan with nonstick cooking spray. Spread squash, sweet peppers, and onion wedges in pan. Toss with olive oil; sprinkle with salt and pepper. Roast, uncovered, 20 to 25 minutes or until tender, stirring once.
Meanwhile, using a vegetable peeler, cut Parmesan cheese in thin strips. Set aside. On lightly floured surface, roll puff pastry to 13x9-inch rectangle. Remove baking pan from oven. Add tomatoes to pan. Toss vegetables with balsamic vinegar and half the Parmesan cheese. Spread vegetables evenly in pan. Lay pastry over vegetables, tucking in edges. Return pan to oven; bake for 15 minutes or until pastry is puffed and golden.
Remove pan from oven; cool 5 minutes. Invert a 15x10x1-inch baking pan over pan with pastry. Carefully invert pans together; remove 13x9 pan. Transfer any vegetables that stick to finished tart. Sprinkle tart evenly with remaining cheese and 2 teaspoons of the thyme. In small bowl stir together dressing, chopped onion, and remaining 1 teaspoon thyme. Cut in squares. Serve tart warm or at room temperature with dressing. Makes 12 servings.