Bring a large pot of salted water to a boil and cook the angel hair pasta until al dente according to package directions; reserve about 1/2 cup pasta cooking water before draining.
Heat a large skillet over low heat and add 6 tablespoons olive oil, minced garlic, and red pepper flakes.
Sauté gently for 2–3 minutes, stirring, until the garlic is fragrant and just turning golden but not browned.
Add the cooked and drained pasta to the skillet with salt, freshly ground black pepper, and 1/2 cup reserved pasta water.
Toss everything together over low heat until the pasta is well coated and the sauce is silky, adding more reserved pasta water a tablespoon at a time if needed.
Serve immediately with extra olive oil and grated Parmesan on top, if desired.
