Place chopped tomatoes in a large serving bowl. Using your hands, squeeze and smash tomatoes to release all of their juices. Combine with olive oil, garlic, basil and salt. Set aside and allow to marinate (even up to an hour).
Cook pasta according to package instructions. Drain.
Immediately add hot pasta to the serving bowl with the tomatoes. Mix to combine.
Serve topped with freshly grated Parmigiano-Reggiano.