Preheat the oven to 450 degrees F. Bring a large pot of water to a boil.
Place all the vegetables except for the tomatoes onto a large heavy baking sheet. Drizzle with oil and sprinkle with dried herbs, salt, and pepper, and toss until all are coated.
Move half of the vegetable mixture to a second baking sheet. Roast in oven until the carrots are tender and the vegetables begin to brown. Flipping or stirring after the first 10 minutes is helpful but not required. Roast about 20 minutes total.
While the vegetables are roasting, cook the pasta until al dente, about 7-8 minutes. Drain the pasta but reserve one cup of the pasta water.
Toss the pasta and roasted vegetables in a large bowl. Add in the cherry tomatoes and just enough of the reserved pasta water to loosen and moisten the dish. Season with additional salt and pepper according to your tastes. Sprinkle with the fresh grated Parmesan and serve immediately.