Buy the Parmigiano-Reggiano in wedges and grate it right before cooking for the best flavor. Slideshow: More Pasta Recipes
Cook spaghetti according to package instructions in a pot of well-salted boiling water.
Meanwhile, in a large skillet set over medium heat, add 1/4 cup of the olive oil. When the oil begins to shimmer, add three-quarters of the garlic and 1/2 teaspoon salt. When garlic starts to smell fragrant, after about 1 minute, add a small splash of the pasta cooking water.
When the spaghetti is done, drain and add to the skillet. Mix well, then add the remaining 2 tablespoons oil, remaining garlic, Parmigiano-Reggiano and a few grinds of black pepper. Mix again and serve.