Bring a large pot of water to a boil and salt it liberally before sliding the pasta in. Cook for 7 to 8 minutes, or until al dente. Drain, reserving 1/2 cup of the starchy cooking water. Pour the pasta back into the pot and drizzle in the reserved oil, discarding the garlic cloves. Toss to combine. Add the parsley, lemon zest, Parmesan cheese, a sprinkle of salt, and a few grinds of pepper. If the pasta seems dry after adding the cheese, add the reserved cooking liquid, 1 tablespoon at a time, and toss to coat. The spaghetti should glisten a bit, but it should not be dripping with oil. Serve with additional cheese grated on top, if desired.