Bring a large pot of water to a boil. Salt the water and drop the spaghetti into the pot.
Heat a large deep skillet over low heat. Add extra-virgin olive oil and garlic and crushed red pepper flakes.
When the pasta has been cooking about 5 minutes, add lemon juice, a ladle of the cooking water from the pasta and the cream to the garlic and oil. Raise heat a bit to bring sauce to a bubble.
Drain pasta when it still has a good bite to it, al dente. Add lemon zest and half of the cheese to the cream sauce. Season the sauce with salt, to taste. Add pasta to pan and turn off heat. Toss the pasta with sauce a minute or 2, allowing it time to soak up the sauce.
Top the plates of pasta or platter with remaining cheese, parsley and basil.