Combine the tomatoes, olive oil, garlic, red pepper flakes, salt, and pepper in a large serving bowl. Cover and let marinate at room temperature for at least 2 hours and up to 4. (Don't refrigerate the marinade — cold kills tomato flavor.)
Bring a large pot of well-salted water to a rolling boil. Cook the angel hair 2 to 3 minutes until just al dente. Reserve 1/2 cup pasta water, then drain.
Add the hot pasta to the marinated tomatoes and toss well for 1 minute — the heat wakes up the garlic and basil and pulls the tomato juices into a sauce.
Add the Parmesan and torn basil; toss again, loosening with pasta water a splash at a time until glossy. Serve immediately in big bowls.