Preheat the oven to 200°.
Wash and dry all the vegetables thoroughly. Clean the zucchini, halve them lengthwise, then quarter them, and start cutting them into small pieces—not too small, but all the same size.
Arrange them in a rectangular glass baking dish suitable for high-heat cooking. Do the same with the aubergines and peppers, peeling them and cutting them into chunks. Add them to the courgettes and stir to distribute the vegetables evenly.
In a bowl, combine the breadcrumbs, basil, thyme, and salt, and grate the cheese. Mix the powders together and use them to evenly coat the vegetables.
Cut the tomatoes in half and grate them, extracting only the powder. Add a pinch of salt and keep the mixture handy.
Shred the mozzarella, spread it over the baking dish, then pour over the tomato sauce you just made. Add a second layer of mozzarella, smooth the surface, and bake for about 45 minutes. Remove from the oven and sprinkle with more Parmesan while still warm, then serve.
