Step 1

Preheat oven to 375 degrees with rack in upper third. Coat a 9-by-13-inch gratin dish with 1 teaspoon oil, and sprinkle with garlic. Using a mandoline or a very sharp knife, slice potatoes and zucchini as thinly as possible into rounds. Arrange potatoes, zucchini, and tomatoes in overlapping layers around prepared dish, and sprinkle with the salt and pepper. Drizzle with remaining 4 teaspoons oil, and sprinkle with thyme and cheese.

Step 2

Cover with foil; bake until potatoes are tender, 35 to 45 minutes. Remove foil; continue baking until top is golden brown, about 25 minutes more. Remove from oven; and serve immediately.