Preheat the oven to 400 degrees. In a colander, toss the eggplant and zucchini with 1 teaspoon of kosher salt and let stand for 20 minutes. Drain well and gently squeeze out any excess liquid.

Meanwhile, in a small bowl, stir the olive oil with the garlic. Coat a 9-by-13-inch baking dish with 1 1/2 teaspoons of the garlic-infused oil. Tear the bread into 2-inch pieces and line the bottom of the baking dish with bread, fitting the pieces tightly together. Drizzle the bread with 2 tablespoons of the garlic oil and season with salt and pepper. Sprinkle the bread with half of the basil.

In a medium bowl, toss the eggplant and zucchini with 2 tablespoons of the garlic oil and season with salt and pepper. Sprinkle the tomato slices with salt and pepper. Arrange the eggplant, zucchini and tomatoes over the bread, overlapping them if necessary. Sprinkle with the thyme leaves, salt, and pepper and drizzle with the remaining garlic oil.

Bake the gratin for about 40 minutes, until the vegetables begin to brown and the bottom of the bread is golden brown. Remove the vegetable gratin from the oven and let stand until cooled slightly, about 10 minutes. Sprinkle with the remaining basil, cut into pieces and serve.

The gratin can be baked up to 2 hours in advance. Reheat in a 350 degrees oven or serve at room temperature.