Preheat oven to 400°F. Spray a 9×13 pan with non-stick spray.

Toss zucchini and summer squash slices with 1 teaspoon of salt in a large bowl, then transfer vegetables to a colander set over a bowl. Let stand until zucchini and squash release at least 3 tablespoons of liquid, about 45 minutes.

Arrange slices on a triple layer of paper towels; cover with another triple layer of paper towels. Firmly press each slice to remove as much liquid as possible.

Place tomato slices in a single layer on double layer paper towels and sprinkle evenly with 1/2 teaspoon of salt; let stand 30 minutes. Place second double layer paper towels on top of tomatoes and press firmly to dry tomatoes.

Meanwhile, heat 1 tablespoon oil in a 12-inch non-stick skillet over medium heat until simmering.

Add onions, remaining 1/2 teaspoon salt, and 1/4 teaspoon pepper; cook, stirring occasionally, until onions are softened and dark golden brown, 20 to 25 minutes. Set onions aside.

Combine garlic, 3 tablespoons oil, remaining 1/2 teaspoon pepper, and thyme in a small bowl.

In large bowl, toss zucchini and summer squash in half of oil mixture, then arrange in greased baking dish.

Arrange caramelized onions in an even layer over squash. Slightly overlap tomato slices in a single layer on top of onions.

Spoon remaining garlic-oil mixture evenly over tomatoes. Bake until vegetables are tender and tomatoes are starting to brown on edges, 40 to 45 minutes.

Combine bread crumbs, mozzarella, and remaining tablespoon oil.

Remove baking dish from oven and increase heat to 450°F. Sprinkle bread crumb mixture evenly on top of tomatoes. Bake gratin until bubbling and until cheese is lightly browned, 5 to 10 minutes. Sprinkle with basil and let sit at room temperature 10 minutes before serving.