Place a large pot of water over high heat and bring to a boil to cook the spaghetti. Once at a boil, add some salt and the spaghetti, and cook to al dente, according to package directions. Drain thoroughly.
While the water is coming up to a boil for the pasta, make the parsley pesto: Place the garlic and parsley leaves in the bowl of a food processor. Add some salt and pepper, and pulse until roughly chopped. With the machine running, pour in 1/3 to 1/2 cup EVOO (just enough to make a thick, smooth paste). Turn the machine off and reserve.