Lay the vegetables and garlic on a baking sheet (will need 2-3 baking sheets). Drizzle with olive oil, salt, and pepper. Bake at 400 for 20-30 minutes.
Bring a large pan of salted water to a boil. Add the pasta and cool al-dente. Reserve about a cup of the pasta water.
Toss the roasted vegetables, tomatoes, and garlic with the cooked linguine. Add in some water, the herbs and mix well. Toss in the Parmesan cheese and more salt and pepper if needed. Serve with more fresh cheese and fresh basil.