Preheat oven to 350 degrees F.
Prepare tomato sauce: Heat 2 tablespoons olive oil in a non-stick saucepan over medium heat. Add chopped onion and saute until soft and translucent, about 5 minutes. Add 4 cloves crushed garlic and saute until fragrant, about 1 minute. Add dried oregano, basil, and parsley and stir. Add crushed tomatoes and salt and simmer until thickened, about 15 minutes.
Meanwhile, in a small bowl, mix together 1/4 cup olive oil, 1 teaspoon minced garlic, and dried thyme. Place zucchini on a sheet pan and brush with olive oil mixture. Bake until soft, about 5 minutes. Remove from the oven and set aside. Marinate the eggplant and yellow squash in the remaining olive oil mixture for a few minutes.
Heat 2 tablespoons olive oil in a non-stick skillet over medium heat. Add 2 cloves minced garlic and saute until fragrant. Add sliced button mushrooms and saute until tender. Set aside. Meanwhile, place marinated vegetables in a roasting pan and roast in the oven for 10 minutes.
Line the bottom of a casserole dish with the baked zucchini slices. Add half of the eggplant and squash mixture. Top with half of the tomato sauce and then spread the ricotta cheese over. Arrange portobello slices over top and then sprinkle with half of the mozzarella. Top with the sauteed mushroom mixture. Top with remaining eggplant and squash mixture. Spread remaining tomato sauce over top. Sprinkle with remaining mozzarella and all of the Parmesan. Bake until the cheese is melted and brown, about 40 minutes. Let stand for 5 minutes before cutting into and serving.