Heat oven to 375 degrees. Heat oil and cook onion until tender and slightly golden, 6 – 8 minutes.
Arrange the onion on the bottom of 9″ X 13″ baking dish. Overlap tomato, squash and potato on top of onion. Season with salt & pepper, sprinkle with thyme and parmesan. Drizzle with more oil.
Bake covered for 30 minutes. Then uncover and bake until golden, about 30 minutes more.