Preheat the oven to 375 degrees F and oil a 7 by 11-inch baking dish.
Heat 2 tablespoons oil in a large skillet over medium-low heat. Cook the onions, garlic and 1 teaspoon salt, stirring, 5 minutes, until soft but not browned. Stir in the basil and thyme and spread in the dish.
Toss the sliced vegetables with the remaining oil, salt and pepper and stand them in alternating compact upright rows on the onions.
Cover with foil and bake until soft, 30 to 35 minutes. Uncover, sprinkle with the Parmesan and bake until the cheese browns, about 20 minutes. Serve hot or at room temperature.