Heat EVOO in a large pot over medium to medium-high heat. Add peppers, zucchini, eggplant, carrot, onion and garlic. Season with thyme, rosemary, salt and pepper. Cook, partially covered, for 7-8 minutes, stirring occasionally. Add tomato paste and stir to combine. Add stock and tomatoes. Break up tomatoes with wooden spoon or potato masher, bring sauce to bubble, add basil and reduce the sauce over low heat for 30 minutes.
Bring a large pot of water to a boil for the pasta; salt the water, cook pasta to al dente. Reserve half a cup of starchy cooking water then drain pasta and add back to pot. Add butter, a few ladles of sauce, the reserved starchy water and toss to combine. Add cheese and toss to coat pasta. Serve pasta in shallow bowls topped with more vegetable sauce and parsley.