When I say the word "pesto" to people in America (or anywhere outside Italy), I know they are thinking of pesto alla Genovese, with its lush green color and intense perfume of fresh basil leaves. Indeed, though there are countless fresh sauces that are also termed "pesto" in Italian cuisine it seems that pasta with basil-and- pine- nut pesto is so well known that it might as well be the national Italian dish! Traditionally, long, flat trenette or shorter twisted trofie is the pasta used here, though even spaghetti is great with the pesto. For the most authentic flavor, use a sweet, small-leaved Genovese basil for the pesto-perhaps you can find it at a farmers' market in summer, or grow it yourself. Large basil will be delicious, too. Of course, use the best extra-virgin olive oil available, in the pesto and on the pasta, preferably pressed from the marvelous taggiasca olives of Liguria.
For the Pesto
3 cups fresh basil leaves, (firmly packed to measure)
3 plump garlic cloves, peeled
½ tablespoons kosher salt
⅓ cup extra-virgin olive oil, (preferably Ligurian), plus more for covering
¼ cup pine nuts, toasted
2 tablespoons Grana Padano, or Parmigianno-Reggiano, grated
2 tablespoons pecorino, grated
For the Pasta
Kosher salt for the pasta pot
½ pound red potatoes, peeled, cut in 1/2-inch chunks
½ pound fresh green beans, ends trimmed cut in 2-inch pieces
1 pound trenette, trofie, or spaghetti
¼ cup pecorino, grated
¼ cup Grana Padano, or Parmigiano-Reggiano grated
To make the pesto: Put all of the basil, the garlic cloves, salt, and olive oil in the food-processor bowl. Process 10 to 15 seconds-stopping once to scrape down the sides of the bowl-to form a coarse paste.
Dump in the pine nuts, and process another 10 seconds or more (scraping down the bowl once or twice), creating a uniformly smooth bright-green paste. Add the grated cheeses to the bowl, and pulse a few times just to blend in. The pesto should be thick yet flowing; if too firm, blend in olive oil, a spoonful at a time, to loosen it.
Scrape the pesto into a small bowl or container, and pour a thin film of olive oil over the top surface to prevent it from discoloring. It can stay at room temperature for a couple of hours before being used. For longer keeping, lay plastic wrap on the surface of the pesto, seal the container, and refrigerate or freeze. Let the pesto return to room temperature before using.
To make the pasta: Bring salted water to a boil in the large pot (at least 6 quarts, with a tablespoon kosher salt). Drop in the potato chunks in boiling water, stir, and cook them for 10 minutes, then add the green beans. Cook the beans and potatoes for another 10 minutes and then add the pasta to the pot and cook 5 minutes until the trennete is al dente.
Set the large skillet over very low heat, just to warm it, or warm the serving bowl, whichever you'll use for dressing the pasta. Scrape the pesto into the pan or bowl, and loosen it with a bit of the pasta boiling water (and don't cook the pesto, just warm it). When the vegetables are tender and the pasta is al dente, lift everything from the pot with a spider and tongs, drain briefly, and drop into the skillet or bowl. (If you prefer, drain the pasta and vegetables into a colander, being sure to reserve a cup or so of pasta cooking water before you pour it out.) Toss pasta, vegetables, and pesto together well-moisten with more pasta water if needed-then sprinkle the grated cheeses over, and toss again. Serve immediately in warm bowls.