Preheat the oven to 400°F.

Place the sliced zucchini, squash, eggplant, and tomatoes on a large sheet pan or cutting board, allowing as much of their surface to be exposed as possible. Sprinkle with ½ teaspoon of the salt and allow to sit for 30 minutes.

Meanwhile, heat a skillet over medium heat. Add 2 teaspoon of the oil and, when it's shimmering, add the onions. Cook for a few minutes, stirring occasionally until they're soft and translucent. Add the garlic and cook for one minute more, stirring frequently. Remove from the heat.

Gently wipe off any water that's accumulated on the surface of the vegetables and pat them dry.

Using a shallow round 8 or 9-inch baking dish, pie pan, or similarly sized baking dish, spread the sautéed onion and garlic in the bottom of the dish.

Arrange the vegetable slices, along with the sliced potato, on their sides 'domino-style', reserving the smaller pieces for the inside of the tian. You can also do this easily by making 'stacks' of the same size of each vegetable (ie. one slice each of potato, tomato, zucchini, eggplant, and squash of the same size, then add that stack all at once to the dish). Continue until the pan is full and all of the slices have been used.

Drizzle the remaining olive oil over the vegetables, then sprinkle the remaining salt, pepper, and Italian seasoning over the top. Cover with foil and bake for 30 minutes.

Remove from the oven and sprinkle with the parmesan cheese. Put back in the oven, uncovered, and bake for another 15 minutes or until the vegetables are cooked through. Serve immediately.