Preheat oven to 350°F.
Spray baking dish with cooking spray.
Fill a large pan with water. Scrub squash and zucchini and add to water. Bring to a low boil over medium heat. Let boil for 5-6 minutes. Squash should be firm on the outside and fork-tender on the inside.
Remove squash and zucchini from water and let cool to touch.
While squash is cooling peel and chop tomato, and onion. Set aside.
When squash and zucchini is cool, slice inhalf long ways. Take knife and gently run alongside the skin of 3 yellow squash and 3 zucchini halves. Use spoon to scoop out cooked pulp. Chop into bite sized pieces Add to chopped tomatoes.
Chop the remaining yellow squash and zucchini halves into bite sized pieces and add to tomato mixture.
Drizzle olive oil, and vinegar over tomato mixture. Sprinkle in salt, pepper, and herbs. Use spoon to gently toss tomato mixture.
Drain squash and zucchini halves. Using a slotted spoon, drain tomatoe mixture before adding to squash and zucchini halves.
Add shredded Parmesan cheese to zucchini.
Place baking dish on bottom rack of oven and cook for 30 minutes.