Bring a large pot of salted water to a boil. Add the spaghetti and cook until al dente, 9 to 11 minutes. Reserve 1 cup pasta water, then drain the pasta.
Meanwhile, heat the olive oil in a large skillet over medium heat. Add the garlic; when it begins to sizzle, add the zucchini and saute for a couple of minutes. Add 1/4 cup of the pasta water and cook until the zucchini is tender, about 5 minutes. Add 1/4 teaspoon salt and half of the basil. Remove the garlic.
Add the pasta to the skillet along with about 1/2 cup of the reserved cooking water; shake the pan vigorously, adding a little more cooking water if the pasta looks dry. Cook, tossing, until the liquid is absorbed, 3 to 4 minutes. Remove from the heat and add the parmigiano, pecorino and the remaining basil; toss. Top with more Parmesan.
Photograph by Ryan Liebe
Recipe courtesy of Katie Lee for Food Network Magazine