Prepare the pesto according to this recipe, using 1/3 cup olive oil.

Bring a large pot of salted water to a boil. Prepare the spaghetti according to the package instructions, cooking until al dente. Reserve 1 cup of the pasta cooking water, then drain.

Transfer the pasta to a large skillet. Add the pesto and 1/2 cup*** of the starchy pasta water and toss to coat, adding more pasta water as needed to coat the pasta in a lightly creamy sauce. If desired, gently warm the pasta over low heat.

Season to taste and serve topped with freshly grated Parmesan and lots of basil.