Combine the halved tomatoes, olive oil, minced garlic, red pepper flakes, salt, black pepper, and chopped basil in a large mixing bowl.
Cover the bowl and let the tomato mixture marinate at room temperature for 4 hours, or at least 2 hours if you are short on time.
Bring a large pot of salted water to a boil.
Cook the angel hair or spaghetti according to the package directions until al dente.
Drain the pasta well and immediately add the hot pasta to the bowl with the marinated tomato mixture.
Toss until the pasta is evenly coated in the tomato juices and olive oil.
Add the grated Parmesan cheese and toss again.
Taste and adjust with extra salt, Parmesan, or olive oil if needed.
Serve immediately with more Parmesan and fresh basil on top.