In a medium skillet, heat the olive oil over medium heat. Add the onions and saute, stirring frequently, until limp and golden brown, about 20 minutes. Reduce the heat to medium-low if they're browning too quickly. Add the garlic and saute; until soft and fragrant, 1 to 2 minutes. Spread the onions and garlic evenly in the bottom of an oiled 2-quart shallow gratin dish (preferably oval). Let cool.

Heat the oven to 375 degrees F. Put the tomato slices on a shallow plate to drain for a few minutes and then discard the collected juices. In a medium bowl, toss the zucchini and squash slices with 1-1/2 tablespoons of the olive oil, 2 tablespoons of the thyme, and 1/2 teaspoon of the salt. Reserve half of the cheese for the top of the gratin. Sprinkle 1 tablespoons of the thyme over the onions in the gratin. Starting at one end of the baking dish, lay a row of slightly overlapping tomato slices across the width of the dish and sprinkle with a little of the cheese. Next, lay a row of zucchini, overlapping the tomatoes by two-thirds, and sprinkle with cheese. Repeat with a row of squash, and then repeat rows, sprinkling each with cheese, until the gratin is full.

Season lightly with pepper and the remaining 1/2 tsp. salt. Drizzle the remaining 1-1/2 Tbs. olive oil over all. Combine the reserved cheese with the remaining 1 Tbs. thyme and sprinkle this over the whole gratin. Cook until well-browned all over and the juices have bubbled for a while and reduced considerably, 65 to 70 min. Let cool for at least 15 minutes before serving.