Salt eggplant and let it drain on kitchen towels.
Preheat oven to 425°F and set racks in the upper and lower third of oven.
On a baking sheet, arrange drained eggplant, zucchini, onions and drizzle with EVOO; season with salt and pepper.
On a second baking sheet, arrange tomatoes, chili pepper, garlic, thyme, salt and pepper, and drizzle liberally with EVOO.
Roast vegetables and tomatoes 20-25 minutes, rotating pans halfway through. Eggplant and zucchini should be browned and tender, and the tomatoes burst.
Bring a large pot of water to a boil for the pasta. Add salt and pasta.
Mash tomatoes, garlic and chilies together in a serving bowl; stir in eggplant and zucchini.
Add half a cup of starchy cooking water to the sauce, drain pasta and add it to the bowl. Toss everything together to combine and adjust seasoning. Serve topped with a few drizzles of EVOO and cheese.