Sprinkle the eggplant cubes with a little salt, then leave in a sieve or colander for 30 minutes to extract the dark, bitter juices.
Preheat the oven to 190 degrees C.
Combine all of the prepared vegetables then place in a large baking dish. If the baking dish is overcrowded with veg, split the veg between two dishes. Drizzle the vegetables with olive oil and sprinkle with salt, pepper and oregano. Toss to thoroughly coat the vegetables. Bake in the oven until the vegetables are very soft, about 45 to 55 minutes.
Meanwhile, during the last 10 minutes of cooking, boil the pasta in boiling salted water until al dente, according to the timing on the packet. Drain.
Remove the vegetables from the oven. In the baking dish, toss the veg with the hot pasta. If desired, add cheese and toss to combine. Season to taste with salt and pepper, then serve straightaway.