Warm the olive oil, whole garlic cloves, and crushed red pepper flakes in a small saucepan over medium-low heat for 10 to 15 minutes, gently swirling occasionally, until the garlic sizzles and turns golden to infuse the oil.
If the garlic burns, discard it and start again with fresh oil and garlic.
Bring a large pot of water to a rolling boil, add a generous amount of salt, then add the spaghetti and cook until al dente, about 7 to 8 minutes (follow package timing if different).
Reserve 1/2 cup of the pasta cooking water, then drain the pasta in a colander.
Return the drained pasta to the pot. Discard the garlic cloves from the infused oil and drizzle the oil over the pasta, tossing to coat.
Add the chopped parsley, lemon zest, and grated vegetarian Parmesan; sprinkle with salt and a few grinds of black pepper and toss to combine.
If the pasta seems dry, add the reserved cooking water a tablespoon at a time, tossing until the pasta is glossy but not dripping with oil.
Serve immediately with additional grated Parmesan if desired.