Bring a large pot of water to a boil and cook pasta according to package directions, reserving ½ cup of the cooking liquid just before the pasta is done.
Meanwhile, place oil, garlic, and anchovies in a large skillet over medium heat. Cook 3 minutes or until garlic is golden and the anchovies have melted into the oil, stirring occasionally.
Add the crushed red pepper and cook, stirring, for 30 seconds. Add the reserved cooking liquid, then add the pasta and toss to coat. Stir in the parsley, lemon juice, and cheese. Season with salt and toss to incorporate everything. Serve sprinkled with additional Parmesan cheese if desired.