Bring a large pot of heavily salted water to a boil. Add the pasta and cook according to the package directions. Drain.

While the pasta is cooking, heat the olive oil in a large skillet over medium-high heat. Add the garlic and cook, stirring, for 30 seconds. Add the tomatoes and cook until they barely start to break down, about 2 minutes. Add the basil and red pepper and toss. Add the pasta and cheeses and toss to coat. Season to taste with salt and pepper and serve immediately with extra Parmesan, if desired.