Toss the zucchini and summer squash with salt in a large colander and set over a bowl to drain for at least 30 minutes, which draws out excess moisture to prevent a soggy gratin.

Arrange the tomato slices on several layers of paper towels and sprinkle with salt. Let them stand for 30 minutes to release their juices, then pat the tops dry with additional paper towels.

Heat a portion of the olive oil in a large skillet over medium-high heat. Add the onions and cook until softened and lightly browned, about 10 to 12 minutes.

Pulse the bread, Parmesan, and shallots in a food processor until the mixture forms coarse crumbs.

Whisk the remaining olive oil with the garlic and thyme in a small bowl to create an aromatic oil.

Pat the zucchini and squash slices dry with paper towels. In a large bowl, toss the dried squash with half of the garlic-thyme oil mixture.

Spread the sautéed onions in an even layer across the bottom of a baking dish. Layer the zucchini and squash over the onions, then arrange the tomato slices in a single layer on top.

Drizzle the remaining garlic-thyme oil over the tomatoes and scatter the breadcrumb mixture evenly over the top.

Bake in a 400-degree oven until the vegetables are tender and the breadcrumbs are golden brown and crisp, about 40 to 45 minutes.

Remove from the oven and sprinkle with fresh basil. Serve warm, once the juices have had a moment to settle.