Bring a large pot of salted water to a boil; cook the pasta until al dente, following the package instructions (but start taste testing the pasta a few minutes earlier than instructed).
Meanwhile, core and finely chop the tomatoes. Thinly slice the zucchini. Chop the basil and parsley. Mince the garlic. If not already grated, grate the Parmesan cheese.
In a large bowl, combine the tomatoes, basil, parsley, and garlic, along with kosher salt and olive oil.
When the pasta is done, drain it and add it to the bowl of tomatoes; add the zucchini and toss well. Add the Parmesan cheese and toss again.
Serve topped with more grated cheese and freshly ground pepper.