Preheat the oven to 375 degrees F.
Brush a 9 by 13 by 2-inch baking dish with olive oil. In a medium
saute pan, heat 2 tablespoons of olive oil and cook the onions over
medium-low heat for 8 to 10 minutes, until translucent. Add the
garlic and cook for another minute. Spread the onion mixture on
the bottom of the baking dish.
Slice the potatoes, zucchini, and tomatoes in 1/4-inch thick slices.
Layer them alternately in the dish on top of the onions, fitting them
tightly, making only 1 layer. Sprinkle with salt, pepper, thyme
leaves, and thyme sprigs and drizzle with 1 more tablespoon of
olive oil. Cover the dish with aluminum foil and bake for 35 to 40
minutes, until the potatoes are tender. Uncover the dish, remove
the thyme sprigs, sprinkle the cheese on top, and bake for another
30 minutes until browned. Serve warm.