Preheat your oven to 375°F (190°C).

In a large skillet, warm 2 tablespoons of olive oil over medium heat.

Introduce the thinly sliced onions and sauté for approximately 8 to 10 minutes, stirring occasionally, until they become soft and lightly caramelized. Incorporate the minced garlic and cook for another minute until it becomes fragrant.

Evenly distribute the onion and garlic mixture across the bottom of a 9x13-inch baking dish.

In a large bowl, combine the sliced tomatoes, zucchini, and yellow summer squash.

Drizzle with 2 tablespoons of olive oil, half of the chopped fresh thyme, ½ teaspoon of salt, and freshly ground black pepper.

Toss gently to coat the vegetables.

Arrange the sliced vegetables in overlapping rows on top of the onion mixture in the baking dish, alternating between the tomatoes, zucchini, and yellow summer squash to create a colorful pattern.

Drizzle the remaining tablespoon of olive oil over the top of the vegetables.

Sprinkle with the remaining chopped thyme, ½ teaspoon of salt, and more freshly ground black pepper.

Generously sprinkle 1 cup of grated Parmesan cheese over the vegetables.

Bake in the preheated oven for 30-35 minutes, or until the vegetables are tender and the cheese is golden brown and bubbly.

Remove the gratin from the oven and sprinkle the remaining ¼ cup of Parmesan cheese on top.

Return the dish to the oven for another 5-7 minutes until the cheese is melted and slightly crispy.

Let the gratin rest for a few minutes before serving.

Garnish with extra thyme if desired and serve warm as a side dish or light main course.