Preheat the oven to 400 degrees Fahrenheit (200 degrees Celsius).
In a skillet over medium heat, sauté the sliced onions and minced garlic in one tablespoon of olive oil until softened and translucent.
Spread the sautéed onion and garlic mixture evenly across the bottom of an 8x8-inch baking dish.
Arrange the sliced vegetables vertically in the dish, tightly alternating layers of potato, zucchini, squash, and tomato until the dish is full.
Drizzle the remaining olive oil over the vegetables and season uniformly with thyme, salt, and pepper.
Cover the baking dish tightly with aluminum foil and bake for 30 minutes.
Remove the foil, sprinkle the Parmesan cheese over the top, and continue baking for 15 to 20 minutes until the vegetables are tender and the top is golden brown.