Preheat your oven to 350°F (180°C). Lightly spray an 8" x 8" or 8" x 11" baking dish with olive oil or non-stick spray.
Wash and slice the zucchini and yellow squash into either full slices or half-moon slices, depending on preference.
Wash, dry, and finely chop the fresh basil. Thinly slice the green onions.
In a large bowl, combine the zucchini, yellow squash, chopped basil, green onions, dried thyme, garlic powder, 1/2 cup grated mozzarella cheese, and 1/2 cup grated Parmesan cheese. Mix well until everything is evenly coated and herbs are well-distributed. Season with salt and freshly ground black pepper to taste.
Transfer the vegetable mixture into the prepared baking dish, spreading it evenly.
Bake uncovered for 25-30 minutes, until the zucchini is mostly tender (a fork should easily pierce the squash).
Remove the dish from the oven and sprinkle the remaining 1/2 cup mozzarella cheese over the top. Add a bit more Parmesan if desired.
Return to the oven and bake for an additional 10-15 minutes, until the cheese is melted, bubbly, and slightly golden.
Serve hot as a side dish or a light main course.