In a small saucepan, combine the olive oil, whole garlic cloves, and crushed red pepper flakes. Warm over medium-low heat and cook gently for 10–15 minutes, swirling occasionally, until the garlic sizzles and turns golden to infuse the oil; remove from heat to continue infusing.
If the garlic burns, discard the oil and start over with fresh oil and garlic.
Bring a large pot of water to a rolling boil, salt liberally, and add the spaghetti. Cook according to package directions for about 7–8 minutes or until al dente.
Reserve 1/2 cup of the pasta cooking water, then drain the spaghetti in a colander.
Return the drained spaghetti to the pot. Discard the garlic cloves from the infused oil and drizzle the oil over the pasta; toss to coat.
Add the chopped parsley, lemon zest, grated Parmesan, a sprinkle of salt, and several grinds of black pepper. Toss to combine.
If the pasta seems dry after adding the cheese, add the reserved cooking water 1 tablespoon at a time, tossing until the spaghetti is glossy but not oily.
Serve immediately with additional grated Parmesan if desired.