Heat oven to 400F.
On a baking sheet, spread out tomatoes and dress with a couple of tablespoons EVOO, thyme, salt and pepper. On a separate sheet pan, arrange zucchini, eggplant, peppers and onions. Dress with EVOO and season with salt and pepper. Roast tomatoes 25-30 minutes until charred and beginning to burst. Remove from oven and separate garlic from tomatoes. When cool enough to touch remove the skins. Roast vegetables until brown at edges and tender.
When vegetables have roasted 15 minutes, bring a large pot of water to a boil for the pasta. Cook pasta to al dente, reserving a cup of starchy cooking liquid.
Place roasted tomatoes in a serving bowl while still hot and mash with garlic using a potato masher. Add reserved starchy water and adjust salt and pepper to taste. Toss with pasta and vegetables. Top the pasta with an extra drizzle of EVOO, parsley and cheese.