Preheat the oven. Set it to 400°F (200°C). Lightly oil a 9x13-inch baking dish or similar casserole.
Make the tomato base. In a bowl, mix crushed tomatoes, minced garlic, 1 tablespoon olive oil, oregano, thyme, red pepper flakes, and a generous pinch of salt and pepper.
Spread this evenly over the bottom of the dish.
Prep the vegetables. Slice eggplant, zucchini, yellow squash, onion, and red pepper into thin, even pieces. Aim for 1/8 to 1/4 inch thick so they cook at the same rate.
Layer the vegetables. Arrange slices in a shingled pattern over the tomato base, alternating colors for a pretty look: eggplant, zucchini, squash, onion, pepper, then repeat. Keep it snug but not crammed.
Season generously. Drizzle 1 tablespoon olive oil over the top.
Sprinkle with salt, black pepper, and an extra pinch of oregano or thyme if you like.
Cover and bake. Cover the dish tightly with foil. Bake for 30 minutes to let the vegetables steam and soften.
Uncover and finish. Remove foil and bake another 20–25 minutes, until the edges are lightly caramelized and the vegetables are tender. If using Parmesan, sprinkle it on during the last 5–10 minutes.
Rest and garnish. Let it sit for 10 minutes out of the oven.
Top with chopped fresh basil or parsley. Taste and adjust salt and pepper.
Serve your way. Enjoy as a side, or make it a meal with crusty bread, polenta, quinoa, or a fried egg on top. A drizzle of good olive oil or a few capers adds a final pop.