Preheat oven to 375 degrees.
Heat half of the olive oil in large skillet over medium-high heat. Add onions and sauté for 6 minutes. Add garlic and sauté for 3 minutes. Brush the bottom and sides of a 9- x 13-inch baking dish with olive oil. Spread onions and garlic on the bottom then alternately layer potatoes, zucchini, eggplant and tomatoes on top.
Sprinkle with chopped thyme and remaining olive oil. Cover with foil and bake for 40 minutes. Remove from oven and sprinkle with Mozzarella. Return to the oven and bake, uncovered, for 20 minutes. Top with grated Parmesan cheese, if desired.
Serve and enjoy!